GitHub

Reference List

The papers cited across the atlas — the rigorous analytic results and methods that QAtlas's closed-form claims are derived from and checked against. Each model's @register cards cite entries here by key; the per-model pages reproduce just the references their own results rest on, and the complete numbered list is below.

Entries are the single source of truth in docs/references.bib; every DOI / arXiv id is machine-checked in CI by doiget verify.

[1]
J. Cardy. Conformal Invariance and Percolation (2001), arXiv:math-ph/0103018.
[2]
P. A. Pearce, J. Rasmussen and J.-B. Zuber. Logarithmic minimal models. Journal of Statistical Mechanics: Theory and Experiment 2006, P11017–P11017 (2006).
[3]
H. Saleur. Polymers and percolation in two dimensions and twisted N = 2 supersymmetry. Nuclear Physics B 382, 486–531 (1992).
[4]
R. Vasseur, J. L. Jacobsen and H. Saleur. Indecomposability parameters in chiral logarithmic conformal field theory. Nuclear Physics B 851, 314–345 (2011).
[5]
F. Kos, D. Poland, D. Simmons-Duffin and A. Vichi. Precision Islands in the Ising and $O(N)$ Models (2016), arXiv:1603.04436.
[6]
F. Kos, D. Poland and D. Simmons-Duffin. Bootstrapping the O(N ) vector models. Journal of High Energy Physics 2014 (2014).
[7]
M. Reehorst, S. Rychkov, D. Simmons-Duffin, B. Sirois, N. Su and B. van Rees. Navigator function for the conformal bootstrap. SciPost Physics 11 (2021).
[8]
D. Simmons-Duffin. The lightcone bootstrap and the spectrum of the 3d Ising CFT. Journal of High Energy Physics 2017 (2017).
[9]
E. Lieb, T. Schultz and D. Mattis. Two soluble models of an antiferromagnetic chain. Annals of Physics 16, 407–466 (1961).
[10]
M. F. Maghrebi, Z.-X. Gong and A. V. Gorshkov. Continuous Symmetry Breaking in 1D Long-Range Interacting Quantum Systems. Physical Review Letters 119 (2017).
[11]
P. Pfeuty. The one-dimensional Ising model with a transverse field. Annals of Physics 57, 79–90 (1970).
[12]
K. Slagle and Y. B. Kim. Quantum field theory of X-cube fracton topological order and robust degeneracy from geometry. Physical Review B 96 (2017).
[13]
S. Vijay, J. Haah and L. Fu. Fracton topological order, generalized lattice gauge theory, and duality. Physical Review B 94 (2016).
[14]
B. Derrida, M. R. Evans, V. Hakim and V. Pasquier. Exact solution of a 1D asymmetric exclusion model using a matrix formulation. Journal of Physics A: Mathematical and General 26, 1493–1517 (1993).
[15]
B. Derrida and J. L. Lebowitz. Exact Large Deviation Function in the Asymmetric Exclusion Process. Physical Review Letters 80, 209–213 (1998).
[16]
M. Kardar, G. Parisi and Y.-C. Zhang. Dynamic Scaling of Growing Interfaces. Physical Review Letters 56, 889–892 (1986).
[17]
W. Brzezicki, J. Dziarmaga and A. M. Oleś. Quantum phase transition in the one-dimensional compass model. Physical Review B 75 (2007).
[18]
A. Kitaev. Anyons in an exactly solved model and beyond. Annals of Physics 321, 2–111 (2006).
[19]
K. I. Kugel' and D. I. Khomskiĭ. The Jahn-Teller effect and magnetism: transition metal compounds. Soviet Physics Uspekhi 25, 231–256 (1982).
[20]
M. E. Fisher. Statistical Mechanics of Dimers on a Plane Lattice. Physical Review 124, 1664–1672 (1961).
[21]
P. W. Kasteleyn. The statistics of dimers on a lattice: I. The number of dimer arrangements on a quadratic lattice. Physica 27, 1209–1225 (1961).
[22]
H. N. Temperley and M. E. Fisher. Dimer problem in statistical mechanics-an exact result. The Philosophical Magazine 6, 1061–1063 (1961).
[23]
E. H. Lieb. Flux Phase of the Half-Filled Band. Physical Review Letters 73, 2158–2161 (1994).
[24]
A. Cavaglià, S. Negro, I. M. Szécsényi and R. Tateo. $T\bar{T}$-deformed 2D quantum field theories. Journal of High Energy Physics 2016 (2016).
[25]
F. Smirnov and A. Zamolodchikov. On space of integrable quantum field theories. Nuclear Physics B 915, 363–383 (2017).
[26]
A. B. Zamolodchikov. Expectation value of composite field $T\bar T$ in two-dimensional quantum field theory.
[27]
G. E. Andrews, R. J. Baxter and P. J. Forrester. Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities. Journal of Statistical Physics 35, 193–266 (1984).
[28]
A. Belavin, A. Polyakov and A. Zamolodchikov. Infinite conformal symmetry in two-dimensional quantum field theory. Nuclear Physics B 241, 333–380 (1984).
[29]
D. A. Huse. Exact exponents for infinitely many new multicritical points. Physical Review B 30, 3908–3915 (1984).
[30]
E. Barouch, B. M. McCoy and M. Dresden. Statistical Mechanics of the XY Model. I. Physical Review A 2, 1075–1092 (1970).
[31]
H. W. Blöte, J. L. Cardy and M. P. Nightingale. Conformal invariance, the central charge, and universal finite-size amplitudes at criticality. Physical Review Letters 56, 742–745 (1986).
[32]
P. Calabrese and J. Cardy. Entanglement entropy and quantum field theory. Journal of Statistical Mechanics: Theory and Experiment 2004, P06002 (2004).
[33]
P. Calabrese and J. Cardy. Entanglement entropy and conformal field theory (2009), arXiv:0905.4013.
[34]
P. Calabrese, F. H. Essler and M. Fagotti. Quantum quench in the transverse field Ising chain: I. Time evolution of order parameter correlators. Journal of Statistical Mechanics: Theory and Experiment 2012, P07016 (2012).
[35]
J. L. Cardy. Operator content of two-dimensional conformally invariant theories. Nuclear Physics B 270, 186–204 (1986).
[36]
B. Damski. Fidelity susceptibility of the quantum Ising model in a transverse field: The exact solution. Physical Review E 87 (2013).
[37]
S.-J. Gu. Fidelity approach to quantum phase transitions. International Journal of Modern Physics B 24, 4371–4458 (2010).
[38]
M. B. Hastings and T. Koma. Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006).
[39]
M. Heyl, A. Polkovnikov and S. Kehrein. Dynamical Quantum Phase Transitions in the Transverse-Field Ising Model. Physical Review Letters 110 (2013).
[40]
M. Heyl. Dynamical quantum phase transitions: a review. Reports on Progress in Physics 81, 054001 (2018).
[41]
E. H. Lieb and D. W. Robinson. The finite group velocity of quantum spin systems. Communications in Mathematical Physics 28, 251–257 (1972).
[42]
L. Onsager. Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition. Physical Review 65, 117–149 (1944).
[43]
I. Peschel. Calculation of reduced density matrices from correlation functions. Journal of Physics A: Mathematical and General 36, L205–L208 (2003).
[44]
M. Rigol, V. Dunjko, V. Yurovsky and M. Olshanii. Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons. Physical Review Letters 98 (2007).
[45]
S. Sachdev. Theory of finite-temperature crossovers near quantum critical points close to, or above, their upper-critical dimension. Physical Review B 55, 142–163 (1997).
[46]
S. Sachdev. Quantum Phase Transitions (2011).
[47]
J. D. Bekenstein. Universal upper bound on the entropy-to-energy ratio for bounded systems. Physical Review D 23, 287–298 (1981).
[48]
V. Bužek and M. Hillery. Quantum copying: Beyond the no-cloning theorem. Physical Review A 54, 1844–1852 (1996).
[49]
J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt. Proposed experiment to test local hidden-variable theories. Physical Review Letters 23, 880–884 (1969).
[50]
J. Maldacena, S. H. Shenker and D. Stanford. A bound on chaos. Journal of High Energy Physics 2016, 106 (2016).
[51]
N. Margolus and L. B. Levitin. The maximum speed of dynamical evolution. Physica D: Nonlinear Phenomena 120, 188–195 (1998).
[52]
N. D. Mermin. Extreme quantum entanglement in a superposition of macroscopically distinct states. Physical Review Letters 65, 1838–1840 (1990).
[53]
Y. Sekino and L. Susskind. Fast scramblers. Journal of High Energy Physics 2008, 065 (2008).
[54]
P. W. Shor and J. Preskill. Simple Proof of Security of the BB84 Quantum Key Distribution Protocol. Physical Review Letters 85, 441–444 (2000).
[55]
I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki. Valence bond ground states in isotropic quantum antiferromagnets. Communications in Mathematical Physics 115, 477–528 (1988).
[56]
D. P. Arovas and A. Auerbach. Extended Heisenberg models of antiferromagnetism: Analogies to the fractional quantum Hall effect. Physical Review Letters 60, 531–534 (1988).
[57]
A. Garcia-Saez, V. Murg and T.-C. Wei. Spectral gaps of Affleck-Kennedy-Lieb-Tasaki Hamiltonians using tensor network methods. Physical Review B 88, 245118 (2013), arXiv:1308.3631.
[58]
T. Kennedy and H. Tasaki. Hidden $Z_2 \times Z_2$ symmetry breaking in Haldane-gap antiferromagnets. Physical Review B 45, 304–307 (1992).
[59]
E. H. Lieb and F. Y. Wu. Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension. Physical Review Letters 20, 1445–1448 (1968).
[60]
M. Nakamura. Tricritical behavior in the extended Hubbard chains. Physical Review B 61, 16377–16392 (2000).
[61]
J. Voit. One-dimensional Fermi liquids. Reports on Progress in Physics 58, 977–1116 (1995).
[62]
R. J. Baxter. Exactly Solved Models in Statistical Mechanics (Academic Press, 1982).
[63]
R. Houtappel. Order-disorder in hexagonal lattices. Physica 16, 425–455 (1950).
[64]
G. H. Wannier. Antiferromagnetism. The Triangular Ising Net. Physical Review 79, 357–364 (1950).
[65]
A. Polyakov. Quantum geometry of bosonic strings. Physics Letters B 103, 207–210 (1981).
[66]
A. Zamolodchikov and A. Zamolodchikov. Conformal bootstrap in Liouville field theory. Nuclear Physics B 477, 577–605 (1996).
[67]
A. Kitaev. A simple model of quantum holography. KITP Program: Entanglement in Strongly-Correlated Quantum Matter (talks) (2015), http://online.kitp.ucsb.edu/online/entangled15/kitaev/.
[68]
J. Maldacena and D. Stanford. Remarks on the Sachdev-Ye-Kitaev model. Physical Review D 94 (2016).
[69]
S. Sachdev and J. Ye. Gapless spin-fluid ground state in a random quantum Heisenberg magnet. Physical Review Letters 70, 3339–3342 (1993).
[70]
Z.-X. Gong, M. Foss-Feig, S. Michalakis and A. V. Gorshkov. Persistence of Locality in Systems with Power-Law Interactions. Physical Review Letters 113 (2014).
[71]
T. Koffel, M. Lewenstein and L. Tagliacozzo. Entanglement Entropy for the Long-Range Ising Chain in a Transverse Field. Physical Review Letters 109 (2012).
[72]
A. Koga and N. Kawakami. Quantum Phase Transitions in the Shastry-Sutherland Model for SrCu$_2$(BO$_3$)$_2$. Physical Review Letters 84, 4461–4464 (2000).
[73]
B. Sriram Shastry and B. Sutherland. Exact ground state of a quantum mechanical antiferromagnet. Physica B+C 108, 1069–1070 (1981).
[74]
M. Freedman, A. Kitaev, M. Larsen and Z. Wang. Topological quantum computation. Bulletin of the American Mathematical Society 40, 31–38 (2002).
[75]
A. Kitaev and J. Preskill. Topological Entanglement Entropy. Physical Review Letters 96 (2006).
[76]
N. Read and E. Rezayi. Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level. Physical Review B 59, 8084–8092 (1999).
[77]
W. Chen, K. Hida and B. C. Sanctuary. Ground-state phase diagram of $S=1$ XXZ chains with uniaxial single-ion-type anisotropy. Physical Review B 67 (2003).
[78]
Y.-C. Tzeng and M.-F. Yang. Scaling properties of fidelity in the spin-1 anisotropic model. Physical Review A 77 (2008).
[79]
S. R. White and D. A. Huse. Numerical renormalization-group study of low-lying eigenstates of the antiferromagnetic $S=1$ Heisenberg chain. Physical Review B 48, 3844–3852 (1993).
[80]
J. L. Cardy. Conformal invariance and surface critical behavior. Nuclear Physics B 240, 514–532 (1984).
[81]
C. N. Yang and T. D. Lee. Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation. Physical Review 87, 404–409 (1952).
[82]
I. Affleck. Universal term in the free energy at a critical point and the conformal anomaly. Physical Review Letters 56, 746–748 (1986).
[83]
I. Affleck. Quantum spin chains and the Haldane gap. Journal of Physics: Condensed Matter 1, 3047–3072 (1989).
[84]
H. Bethe. Zur Theorie der Metalle. Zeitschrift f�r Physik 71, 205–226 (1931).
[85]
S. Eggert, I. Affleck and M. Takahashi. Susceptibility of the spin 1/2 Heisenberg antiferromagnetic chain. Physical Review Letters 73, 332–335 (1994).
[86]
F. D. Haldane. General Relation of Correlation Exponents and Spectral Properties of One-Dimensional Fermi Systems: Application to the Anisotropic $S=1/2$ Heisenberg Chain. Physical Review Letters 45, 1358–1362 (1980).
[87]
L. Hulthén. Über das Austauschproblem eines Kristalles. Arkiv för Matematik, Astronomi och Fysik 26A, 1–106 (1938).
[88]
A. Luther and I. Peschel. Calculation of critical exponents in two dimensions from quantum field theory in one dimension. Physical Review B 12, 3908–3917 (1975).
[89]
G. Müller, H. Thomas, H. Beck and J. C. Bonner. Quantum spin dynamics of the antiferromagnetic linear chain in zero and nonzero magnetic field. Physical Review B 24, 1429–1467 (1981).
[90]
J. des Cloizeaux and J. J. Pearson. Spin-Wave Spectrum of the Antiferromagnetic Linear Chain. Physical Review 128, 2131–2135 (1962).
[91]
C. N. Yang. The Spontaneous Magnetization of a Two-Dimensional Ising Model. Physical Review 85, 808–816 (1952).
[92]
R. J. Baxter. One-dimensional anisotropic Heisenberg chain. Annals of Physics 70, 323–337 (1972).
[93]
B. M. McCoy and T. T. Wu. Two-dimensional Ising field theory in a magnetic field: Breakup of the cut in the two-point function. Physical Review D 18, 1259–1267 (1978).
[94]
C. N. Yang and C. P. Yang. One-Dimensional Chain of Anisotropic Spin-Spin Interactions. II. Properties of the Ground-State Energy Per Lattice Site for an Infinite System. Physical Review 150, 327–339 (1966).
[95]
S. Elitzur, R. B. Pearson and J. Shigemitsu. Phase structure of discrete Abelian spin and gauge systems. Physical Review D 19, 3698–3714 (1979).
[96]
J. V. José, L. P. Kadanoff, S. Kirkpatrick and D. R. Nelson. Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model. Physical Review B 16, 1217–1241 (1977).
[97]
N. Andrei and J. H. Lowenstein. Diagonalization of the Chiral-Invariant Gross-Neveu Hamiltonian. Physical Review Letters 43, 1698–1701 (1979).
[98]
D. J. Gross and A. Neveu. Dynamical symmetry breaking in asymptotically free field theories. Physical Review D 10, 3235–3253 (1974).
[99]
L. Pauling. The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement. Journal of the American Chemical Society 57, 2680–2684 (1935).
[100]
F. H. Essler, H. Frahm, F. Göhmann, A. Klümper and V. E. Korepin. The One-Dimensional Hubbard Model (2005).
[101]
G. Jüttner, A. Klümper and J. Suzuki. The Hubbard chain at finite temperatures: ab initio calculations of Tomonaga-Luttinger liquid properties. Nuclear Physics B 522, 471–502 (1998), arXiv:cond-mat/9711310.
[102]
A. A. Ovchinnikov. Excitation spectrum in the one-dimensional Hubbard model. Soviet Physics JETP 30, 1160 (1970).
[103]
B. S. Cirel'son. Quantum generalizations of Bell's inequality. Letters in Mathematical Physics 4, 93–100 (1980).
[104]
S. Popescu and D. Rohrlich. Quantum nonlocality as an axiom. Foundations of Physics 24, 379–385 (1994).
[105]
A. Klümper. Thermodynamics of the anisotropic spin-1/2 Heisenberg chain and related quantum chains. Zeitschrift für Physik B Condensed Matter 91, 507–519 (1993).
[106]
A. Lohmann, H.-J. Schmidt and J. Richter. Tenth-order high-temperature expansion for the susceptibility and the specific heat of spin-$s$ Heisenberg models with arbitrary exchange patterns. Physical Review B 89, 014415 (2014).
[107]
J. Lou, T. Xiang and Z. Su. Thermodynamics of the Bilinear-Biquadratic Spin-One Heisenberg Chain. Physical Review Letters 85, 2380–2383 (2000).
[108]
J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker, D. Stanford, A. Streicher and M. Tezuka. Black Holes and Random Matrices (2016), arXiv:1611.04650.
[109]
M. Takahashi. Thermodynamics of One-Dimensional Solvable Models (Cambridge University Press, 1999).
[110]
T. Giamarchi. Quantum Physics in One Dimension (Oxford University Press, 2003).
[111]
P. Coleman. Introduction to Many-Body Physics (Cambridge University Press, 2015).
[112]
G. D. Mahan. Many-Particle Physics (Springer US, 2000).
[113]
P. Calabrese and J. Cardy. Evolution of entanglement entropy in one-dimensional systems. Journal of Statistical Mechanics: Theory and Experiment 2005, P04010 (2005).
[114]
C. K. Majumdar and D. K. Ghosh. On Next-Nearest-Neighbor Interaction in Linear Chain. I. Journal of Mathematical Physics 10, 1388–1398 (1969).
[115]
S. R. White and I. Affleck. Dimerization and incommensurate spiral spin correlations in the zigzag spin chain: Analogies to the Kondo lattice. Physical Review B 54, 9862–9869 (1996).
[116]
S. Eggert. Numerical evidence for multiplicative logarithmic corrections from marginal operators. Physical Review B 54, R9612–R9615 (1996).
[117]
O. Schramm. Scaling limits of loop-erased random walks and uniform spanning trees. Israel Journal of Mathematics 118, 221–288 (2000).
[118]
V. Beffara. The dimension of the SLE curves. The Annals of Probability 36 (2008).
[119]
E. Verlinde. Fusion rules and modular transformations in 2D conformal field theory. Nuclear Physics B 300, 360–376 (1988).
[120]
E. Witten. Quantum field theory and the Jones polynomial. Communications in Mathematical Physics 121, 351–399 (1989).
[121]
N. Read and D. Green. Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect. Physical Review B 61, 10267–10297 (2000).
[122]
C. Nayak, S. H. Simon, A. Stern, M. Freedman and S. Das Sarma. Non-Abelian anyons and topological quantum computation. Reviews of Modern Physics 80, 1083–1159 (2008).
[123]
E. H. Lieb. Exact Solution of the Problem of the Entropy of Two-Dimensional Ice. Physical Review Letters 18, 692–694 (1967).
[124]
E. H. Lieb. Exact Solution of the Two-Dimensional Slater KDP Model of a Ferroelectric. Physical Review Letters 19, 108–110 (1967).
[125]
E. H. Lieb. Exact Solution of the F Model of an Antiferroelectric. Physical Review Letters 18, 1046–1048 (1967).
[126]
B. Sutherland. Exact Solution of a Two-Dimensional Model for Hydrogen-Bonded Crystals. Physical Review Letters 19, 103–104 (1967).
[127]
F. H. Essler and M. Fagotti. Quench dynamics and relaxation in isolated integrable quantum spin chains. Journal of Statistical Mechanics: Theory and Experiment 2016, 064002 (2016).
[128]
S. Coleman, R. Jackiw and L. Susskind. Charge shielding and quark confinement in the massive schwinger model. Annals of Physics 93, 267–275 (1975).
[129]
J. Schwinger. Gauge Invariance and Mass. II. Physical Review 128, 2425–2429 (1962).
[130]
C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn and Z. Papić. Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations. Physical Review B 98 (2018).
[131]
C.-J. Lin and O. I. Motrunich. Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain. Physical Review Letters 122 (2019).
[132]
T. Iadecola, M. Schecter and S. Xu. Quantum many-body scars from magnon condensation. Physical Review B 100 (2019).
[133]
F. M. Surace, P. P. Mazza, G. Giudici, A. Lerose, A. Gambassi and M. Dalmonte. Lattice Gauge Theories and String Dynamics in Rydberg Atom Quantum Simulators. Physical Review X 10 (2020).
[134]
M. Toda. Vibration of a Chain with Nonlinear Interaction. Journal of the Physical Society of Japan 22, 431–436 (1967).
[135]
H. Flaschka. The Toda lattice. II. Existence of integrals. Physical Review B 9, 1924–1925 (1974).
[136]
C. N. Yang and C. P. Yang. Thermodynamics of a One-Dimensional System of Bosons with Repulsive Delta-Function Interaction. Journal of Mathematical Physics 10, 1115–1122 (1969).
[137]
E. Ising. Beitrag zur Theorie des Ferromagnetismus. Zeitschrift für Physik 31, 253–258 (1925).
[138]
S. G. BRUSH. History of the Lenz-Ising Model. Reviews of Modern Physics 39, 883–893 (1967).
[139]
H. Nishimori. Internal Energy, Specific Heat and Correlation Function of the Bond-Random Ising Model. Progress of Theoretical Physics 66, 1169–1181 (1981).
[140]
S. F. Edwards and P. W. Anderson. Theory of spin glasses. Journal of Physics F: Metal Physics 5, 965–974 (1975).
[141]
Y. Imry and S.-k. Ma. Random-Field Instability of the Ordered State of Continuous Symmetry. Physical Review Letters 35, 1399–1401 (1975).
[142]
A. Honecker, M. Picco and P. Pujol. Universality Class of the Nishimori Point in the 2D $\pm J$ Random-Bond Ising Model. Physical Review Letters 87 (2001).
[143]
J. Bricmont and A. Kupiainen. Lower critical dimension for the random-field Ising model. Physical Review Letters 59, 1829–1832 (1987).
[144]
J. Z. Imbrie. The ground state of the three-dimensional random-field Ising model. Communications in Mathematical Physics 98, 145–176 (1985).
[145]
D. Sherrington and S. Kirkpatrick. Solvable Model of a Spin-Glass. Physical Review Letters 35, 1792–1796 (1975).
[146]
G. Parisi. The order parameter for spin glasses: a function on the interval 0-1. Journal of Physics A: Mathematical and General 13, 1101–1112 (1980).
[147]
M. Talagrand. The Parisi formula. Annals of Mathematics 163, 221–263 (2006).
[148]
A. Crisanti and T. Rizzo. Analysis of the $\infty$-replica symmetry breaking solution of the Sherrington-Kirkpatrick model. Physical Review E 65 (2002).
[149]
J. L. Cardy. Conformal invariance and the Yang-Lee edge singularity in two dimensions. Physical Review Letters 54, 1354–1356 (1985).
[150]
J. L. Cardy. Boundary conditions, fusion rules and the Verlinde formula. Nuclear Physics B 324, 581–596 (1989).
[151]
J. Cardy. SLE for theoretical physicists. Annals of Physics 318, 81–118 (2005).
[152]
D. Friedan, Z. Qiu and S. Shenker. Conformal Invariance, Unitarity, and Critical Exponents in Two Dimensions. Physical Review Letters 52, 1575–1578 (1984).
[153]
V. Knizhnik and A. Zamolodchikov. Current algebra and Wess-Zumino model in two dimensions. Nuclear Physics B 247, 83–103 (1984).
[154]
I. Affleck and A. W. Ludwig. Universal noninteger ‘‘ground-state degeneracy’’ in critical quantum systems. Physical Review Letters 67, 161–164 (1991).
[155]
D. Friedan and A. Konechny. Boundary Entropy of One-Dimensional Quantum Systems at Low Temperature. Physical Review Letters 93 (2004).
[156]
M. Bauer and D. Bernard. 2D growth processes: SLE and Loewner chains. Physics Reports 432, 115–221 (2006).
[157]
H. J. Schulz. Phase diagrams and correlation exponents for quantum spin chains of arbitrary spin quantum number. Physical Review B 34, 6372–6385 (1986).
[158]
I. Affleck and M. Oshikawa. Field-induced gap in Cu benzoate and other $S=1/2$ antiferromagnetic chains. Physical Review B 60, 1038–1056 (1999).
[159]
I. Dzyaloshinsky. A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. Journal of Physics and Chemistry of Solids 4, 241–255 (1958).
[160]
T. Moriya. Anisotropic Superexchange Interaction and Weak Ferromagnetism. Physical Review 120, 91–98 (1960).
[161]
A. Y. Kitaev. Unpaired Majorana fermions in quantum wires. Physics-Uspekhi 44, 131–136 (2001).
[162]
W. P. Su, J. R. Schrieffer and A. J. Heeger. Solitons in Polyacetylene. Physical Review Letters 42, 1698–1701 (1979).
[163]
A. Kitaev. Fault-tolerant quantum computation by anyons. Annals of Physics 303, 2–30 (2003).
[164]
M. Levin and X.-G. Wen. Detecting Topological Order in a Ground State Wave Function. Physical Review Letters 96 (2006).
[165]
J. Alicea. New directions in the pursuit of Majorana fermions in solid state systems. Reports on Progress in Physics 75, 076501 (2012).
[166]
J. K. Asbóth, L. Oroszlány and A. Pályi. A Short Course on Topological Insulators (2016).
[167]
H. J. Briegel and R. Raussendorf. Persistent Entanglement in Arrays of Interacting Particles. Physical Review Letters 86, 910–913 (2001).
[168]
J. G. Rau, E. K.-H. Lee and H.-Y. Kee. Generic Spin Model for the Honeycomb Iridates beyond the Kitaev Limit. Physical Review Letters 112 (2014).
[169]
Y. Iqbal, F. Becca, S. Sorella and D. Poilblanc. Gapless spin-liquid phase in the kagome spin-$1/2$ Heisenberg antiferromagnet. Physical Review B 87 (2013).
[170]
S. Depenbrock, I. P. McCulloch and U. Schollwöck. Nature of the Spin-Liquid Ground State of the $S=1/2$ Heisenberg Model on the Kagome Lattice. Physical Review Letters 109 (2012).
[171]
H.-C. Jiang, Z. Wang and L. Balents. Identifying topological order by entanglement entropy. Nature Physics 8, 902–905 (2012).
[172]
S. Yan, D. A. Huse and S. R. White. Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet. Science 332, 1173–1176 (2011).
[173]
F. Verstraete and J. I. Cirac. Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions.
[174]
N. W. Ashcroft and N. D. Mermin. Solid State Physics (Holt, Rinehart and Winston, 1976).
[175]
H. E. Stanley. Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, 1971).
[176]
L. D. Landau and E. M. Lifshitz. Statistical Physics, Part 1. 3 Edition, Vol. 5 of Course of Theoretical Physics (Pergamon Press, 1980).
[177]
L. D. Landau. On the theory of phase transitions. Zh. Eksp. Teor. Fiz. 7, 19–32 (1937).
[178]
V. A. Fateev and A. B. Zamolodchikov. Nonlocal (parafermion) currents in two-dimensional conformal quantum field theory and self-dual critical points in $Z_N$-symmetric statistical systems. Sov. Phys. JETP 62, 215–225 (1985).
[179]
F. D. Haldane. Exact Jastrow-Gutzwiller resonating-valence-bond ground state of the spin-1/2 antiferromagnetic Heisenberg chain with 1/r² exchange. Physical Review Letters 60, 635–638 (1988).
[180]
B. S. Shastry. Exact solution of an S=1/2 Heisenberg antiferromagnetic chain with long-ranged interactions. Physical Review Letters 60, 639–642 (1988).
[181]
L. Mandelstam and I. Tamm. The Uncertainty Relation Between Energy and Time in Non-relativistic Quantum Mechanics. Journal of Physics (USSR) 9, 249–254 (1945).
[182]
W. P. Su, J. R. Schrieffer and A. J. Heeger. Soliton excitations in polyacetylene. Physical Review B 22, 2099–2111 (1980).
[183]
M. Karbach, G. Müller, A. H. Bougourzi, A. Fledderjohann and K.-H. Mütter. Two-spinon dynamic structure factor of the one-dimensional s= Heisenberg antiferromagnet. Physical Review B 55, 12510–12517 (1997).
[184]
I. Pérez Castillo. The exact two-spinon longitudinal dynamical structure factor of the anisotropic XXZ model (2020), arXiv:2005.10729 [cond-mat.str-el].
[185]
J. Korringa. Nuclear magnetic relaxation and resonance line shift in metals. Physica 16, 601–610 (1950).
[186]
R. Chitra and T. Giamarchi. Critical properties of gapped spin-chains and ladders in a magnetic field. Physical Review B 55, 5816–5826 (1997).
[187]
D. S. Fisher. Random transverse field Ising spin chains. Physical Review Letters 69, 534–537 (1992).
[188]
D. S. Fisher. Critical behavior of random transverse-field Ising spin chains. Physical Review B 51, 6411–6461 (1995).
[189]
G. Refael and J. E. Moore. Entanglement entropy of random quantum critical points in one dimension. Physical Review Letters 93, 260602 (2004).
[190]
I. R. Klebanov, S. S. Pufu and B. R. Safdi. F-Theorem without Supersymmetry. Journal of High Energy Physics 2011, 038 (2011), arXiv:1105.4598.
[191]
S. S. Pufu. The F-Theorem and F-Maximization. Journal of Physics A: Mathematical and Theoretical 50, 443008 (2017), arXiv:1608.02960.
[192]
P. Bueno, R. C. Myers and W. Witczak-Krempa. Universality of Corner Entanglement in Conformal Field Theories. Physical Review Letters 115, 021602 (2015), arXiv:1505.04804.
[193]
S. M. Chester. Weizmann Lectures on the Numerical Conformal Bootstrap (2020), arXiv:1907.05147 [hep-th].