S. Furukawa and G. Misguich, Topological entanglement entropy in the quantum dimer model on the triangular lattice, Physical Review B, vol.75, issue.21, p.214407, 2007.
DOI : 10.1103/PhysRevB.75.214407

J. Stéphan, S. Furukawa, G. Misguich, and V. Pasquier, Shannon and entanglement entropies of one- and two-dimensional critical wave functions, Physical Review B, vol.80, issue.18, p.184421, 2009.
DOI : 10.1103/PhysRevB.80.184421

J. Stéphan, G. Misguich, and F. Alet, and Ising chains, Physical Review B, vol.82, issue.18, p.180406, 2010.
DOI : 10.1103/PhysRevB.82.180406

J. Stéphan, G. Misguich, and V. Pasquier, R??nyi entropy of a line in two-dimensional Ising models, Physical Review B, vol.82, issue.12, p.125455, 2010.
DOI : 10.1103/PhysRevB.82.125455

J. Stéphan, G. Misguich, and V. Pasquier, Phase transition in the R??nyi-Shannon entropy of Luttinger liquids, Physical Review B, vol.84, issue.19, 2011.
DOI : 10.1103/PhysRevB.84.195128

J. Stéphan, G. Misguich, and V. Pasquier, R??nyi entanglement entropies in quantum dimer models: from criticality to topological order, Journal of Statistical Mechanics: Theory and Experiment, vol.2012, issue.02, pp.200310-1088, 2003.
DOI : 10.1088/1742-5468/2012/02/P02003

J. Eisert, M. Cramer, and M. B. Plenio, : Area laws for the entanglement entropy, Reviews of Modern Physics, vol.82, issue.1, 2010.
DOI : 10.1103/RevModPhys.82.277

J. D. Bekenstein, Black Holes and Entropy, Physical Review D, vol.7, issue.8, p.2333, 1973.
DOI : 10.1103/PhysRevD.7.2333

M. B. Hastings, An area law for one-dimensional quantum systems, Journal of Statistical Mechanics: Theory and Experiment, vol.2007, issue.08, pp.802410-1088, 2007.
DOI : 10.1088/1742-5468/2007/08/P08024

S. R. White, Density matrix formulation for quantum renormalization groups, Physical Review Letters, vol.69, issue.19, p.2863, 1992.
DOI : 10.1103/PhysRevLett.69.2863

U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Annals of Physics, vol.326, issue.1, 2011.
DOI : 10.1016/j.aop.2010.09.012

E. Stoudenmire and S. R. White, Studying Two-Dimensional Systems with the Density Matrix Renormalization Group, Annual Review of Condensed Matter Physics, vol.3, issue.1, 2012.
DOI : 10.1146/annurev-conmatphys-020911-125018

Y. Shi, L. Duan, and G. Vidal, Classical simulation of quantum many-body systems with a tree tensor network, Physical Review A, vol.74, issue.2, p.22320, 2006.
DOI : 10.1103/PhysRevA.74.022320

G. Vidal, Class of Quantum Many-Body States That Can Be Efficiently Simulated, Physical Review Letters, vol.101, issue.11, p.110501, 2008.
DOI : 10.1103/PhysRevLett.101.110501

C. Holzhey, F. Larsen, and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nuclear Physics B, vol.424, issue.3, pp.443-467, 1994.
DOI : 10.1016/0550-3213(94)90402-2

P. Calabrese and J. Cardy, Entanglement entropy and quantum field theory, Journal of Statistical Mechanics: Theory and Experiment, vol.2004, issue.06, pp.600210-1088, 2004.
DOI : 10.1088/1742-5468/2004/06/P06002

M. M. Wolf, Violation of the Entropic Area Law for Fermions, Physical Review Letters, vol.96, issue.1, p.10404, 2006.
DOI : 10.1103/PhysRevLett.96.010404

E. Fradkin and J. E. Moore, Entanglement Entropy of 2D Conformal Quantum Critical Points: Hearing the Shape of a Quantum Drum, Physical Review Letters, vol.97, issue.5, pp.5040410-1103, 2006.
DOI : 10.1103/PhysRevLett.97.050404

X. G. Wen and Q. Niu, Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces, Physical Review B, vol.41, issue.13, p.9377, 1990.
DOI : 10.1103/PhysRevB.41.9377

L. Balents, Spin liquids in frustrated magnets, Nature, vol.68, issue.7286, p.199, 2010.
DOI : 10.1038/nature08917

G. Misguich, Quantum spin liquids, Exact Methods in Low-dimensional Statistical Physics and Quantum Computing of Lecture Notes of the Les Houches Summer School, 2008.

G. Misguich, Quantum Spin Liquids and Fractionalization Introduction to Frustrated Magnetism -Materials, Experiments, Theory, volume 164 of Springer Series in Solid-State Sciences, pp.407-435, 2011.

A. Kitaev and J. Preskill, Topological Entanglement Entropy, Physical Review Letters, vol.96, issue.11, p.110404, 2006.
DOI : 10.1103/PhysRevLett.96.110404

M. Levin and X. Wen, Detecting Topological Order in a Ground State Wave Function, Physical Review Letters, vol.96, issue.11, p.110405, 2006.
DOI : 10.1103/PhysRevLett.96.110405

A. Hamma, R. Ionicioiu, and P. Zanardi, Bipartite entanglement and entropic boundary law in lattice spin systems, Physical Review A, vol.71, issue.2, p.22315, 2005.
DOI : 10.1103/PhysRevA.71.022315

A. Hamma, R. Ionicioiu, and P. Zanardi, Ground state entanglement and geometric entropy in the Kitaev model, Physics Letters A, vol.337, issue.1-2, 2005.
DOI : 10.1016/j.physleta.2005.01.060

Y. Zhang, T. Grover, A. Turner, M. Oshikawa, and A. Vishwanath, Quasiparticle statistics and braiding from ground-state entanglement, Physical Review B, vol.85, issue.23, p.235151, 2012.
DOI : 10.1103/PhysRevB.85.235151

S. V. Isakov, M. B. Hastings, and R. G. Melko, Topological entanglement entropy of a Bose???Hubbard spin liquid, Nature Physics, vol.4, issue.10, p.77210, 1038.
DOI : 10.1103/PhysRevB.65.054508

S. Yan, D. A. Huse, and S. R. White, Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet, Science, vol.332, issue.6034, p.1173, 2011.
DOI : 10.1126/science.1201080

H. Jiang, Z. Wang, and L. Balents, Identifying topological order by entanglement entropy, Nature Physics, vol.8, issue.12, p.902, 2012.
DOI : 10.1103/PhysRevLett.109.067201

S. Depenbrock, I. P. Mcculloch, and U. Schollwöck, Heisenberg Model on the Kagome Lattice, Physical Review Letters, vol.109, issue.6, p.67201, 2012.
DOI : 10.1103/PhysRevLett.109.067201

S. Nishimoto, N. Shibata, and C. Hotta, Controlling frustrated liquids and solids with an applied field in a kagome Heisenberg antiferromagnet, Nature Communications, vol.4, pp.10-1038, 2013.
DOI : 10.1103/PhysRevLett.69.2863

H. Li and F. D. Haldane, Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States, Physical Review Letters, vol.101, issue.1, p.10504, 2008.
DOI : 10.1103/PhysRevLett.101.010504

X. Qi, H. Katsura, and A. W. Ludwig, General Relationship between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States, Physical Review Letters, vol.108, issue.19, pp.10-1103, 2012.
DOI : 10.1103/PhysRevLett.108.196402

F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, Entanglement spectrum of a topological phase in one dimension, Physical Review B, vol.81, issue.6, p.64439, 2010.
DOI : 10.1103/PhysRevB.81.064439

L. Fidkowski, Entanglement Spectrum of Topological Insulators and Superconductors, Physical Review Letters, vol.104, issue.13, p.130502, 2010.
DOI : 10.1103/PhysRevLett.104.130502

D. Poilblanc, Entanglement Spectra of Quantum Heisenberg Ladders, Physical Review Letters, vol.105, issue.7, p.77202, 2010.
DOI : 10.1103/PhysRevLett.105.077202

URL : https://hal.archives-ouvertes.fr/hal-00485946

A. M. Läuchli and J. Schliemann, spin chains in a ladder geometry, Physical Review B, vol.85, issue.5, p.54403, 2012.
DOI : 10.1103/PhysRevB.85.054403

R. Thomale, A. Sterdyniak, N. Regnault, and B. A. Bernevig, Entanglement Gap and a New Principle of Adiabatic Continuity, Physical Review Letters, vol.104, issue.18, p.180502, 2010.
DOI : 10.1103/PhysRevLett.104.180502

URL : https://hal.archives-ouvertes.fr/hal-00522211

A. M. Läuchli, E. J. Bergholtz, J. Suorsa, and M. Haque, Disentangling Entanglement Spectra of Fractional Quantum Hall States on Torus Geometries, Physical Review Letters, vol.104, issue.15, p.156404, 2010.
DOI : 10.1103/PhysRevLett.104.156404

P. Calabrese and A. Lefevre, Entanglement spectrum in one-dimensional systems, Physical Review A, vol.78, issue.3, p.32329, 2008.
DOI : 10.1103/PhysRevA.78.032329

A. M. Läuchli, Operator content of real-space entanglement spectra at conformal critical points, 2013.

M. A. Metlitski and T. Grover, Entanglement Entropy of Systems with Spontaneously Broken Continuous Symmetry, 2011.

V. Alba, M. Haque, and A. M. Läuchli, Entanglement Spectrum of the Two-Dimensional Bose-Hubbard Model, Physical Review Letters, vol.110, issue.26, p.260403, 2013.
DOI : 10.1103/PhysRevLett.110.260403

Y. He, D. Sheng, and Y. Chen, Chiral Spin Liquid in a Frustrated Anisotropic Kagome Heisenberg Model, Physical Review Letters, vol.112, issue.13, p.137202, 2014.
DOI : 10.1103/PhysRevLett.112.137202

S. Ryu and T. Takayanagi, Holographic Derivation of Entanglement Entropy from the anti???de Sitter Space/Conformal Field Theory Correspondence, Physical Review Letters, vol.96, issue.18, p.181602, 2006.
DOI : 10.1103/PhysRevLett.96.181602

H. Casini and M. Huerta, Renormalization group running of the entanglement entropy of a circle, Physical Review D, vol.85, issue.12, p.125016, 2012.
DOI : 10.1103/PhysRevD.85.125016

. Wen, Stability of U(1) spin liquids in two dimensions, Phys. Rev. B, vol.70, p.214437, 2004.

M. Hermele, T. Senthil, and M. P. Fisher, Algebraic spin liquid as the mother of many competing orders, Physical Review B, vol.72, issue.10, 2005.
DOI : 10.1103/PhysRevB.72.104404

T. Grover, Entanglement Monotonicity and the Stability of Gauge Theories in Three Spacetime Dimensions, Physical Review Letters, vol.112, issue.15, p.151601, 2014.
DOI : 10.1103/PhysRevLett.112.151601

E. Fradkin, D. A. Huse, R. Moessner, V. Oganesyan, and S. L. Sondhi, Bipartite Rokhsar???Kivelson points and Cantor deconfinement, Physical Review B, vol.69, issue.22, p.224415, 2004.
DOI : 10.1103/PhysRevB.69.224415

URL : https://hal.archives-ouvertes.fr/hal-00298552

D. J. Luitz, F. Alet, and N. Laflorencie, Universal Behavior beyond Multifractality in Quantum Many-Body Systems, Physical Review Letters, vol.112, issue.5, p.57203, 2014.
DOI : 10.1103/PhysRevLett.112.057203

URL : https://hal.archives-ouvertes.fr/hal-00982452

D. S. Rokhsar and S. A. Kivelson, Superconductivity and the Quantum Hard-Core Dimer Gas, Physical Review Letters, vol.61, issue.20, pp.237610-1103, 1988.
DOI : 10.1103/PhysRevLett.61.2376

P. W. Leung, K. C. Chiu, and K. J. Runge, Columnar dimer and plaquette resonating-valence-bond orders in the quantum dimer model, Physical Review B, vol.54, issue.18, p.12938, 1996.
DOI : 10.1103/PhysRevB.54.12938

O. F. Syljuåsen, Plaquette phase of the square-lattice quantum dimer model: Quantum Monte Carlo calculations, Physical Review B, vol.73, issue.24, p.245105, 2006.
DOI : 10.1103/PhysRevB.73.245105

A. Ralko, D. Poilblanc, and R. Moessner, Generic Mixed Columnar-Plaquette Phases in Rokhsar-Kivelson Models, Physical Review Letters, vol.100, issue.3, p.37201, 2008.
DOI : 10.1103/PhysRevLett.100.037201

URL : https://hal.archives-ouvertes.fr/hal-00177461

E. Ardonne, P. Fendley, and E. Fradkin, Topological order and conformal quantum critical points, Annals of Physics, vol.310, issue.2, 2004.
DOI : 10.1016/j.aop.2004.01.004

C. L. Henley, From classical to quantum dynamics at Rokhsar???Kivelson points, Journal of Physics: Condensed Matter, vol.16, issue.11, p.891, 2004.
DOI : 10.1088/0953-8984/16/11/045

C. Castelnovo, C. Chamon, C. Mudry, and P. Pujol, From quantum mechanics to classical statistical physics: Generalized Rokhsar???Kivelson Hamiltonians and the ???Stochastic Matrix Form??? decomposition, Annals of Physics, vol.318, issue.2, p.316, 2005.
DOI : 10.1016/j.aop.2005.01.006

M. B. Hastings, I. González, A. B. Kallin, and R. G. Melko, Measuring Renyi Entanglement Entropy in Quantum Monte??Carlo Simulations, Physical Review Letters, vol.104, issue.15, p.157201, 2010.
DOI : 10.1103/PhysRevLett.104.157201

P. Kasteleyn, The statistics of dimers on a lattice, Physica, vol.27, issue.12, pp.1209-1225, 1961.
DOI : 10.1016/0031-8914(61)90063-5

M. E. Fisher, Statistical Mechanics of Dimers on a Plane Lattice, Physical Review, vol.124, issue.6, p.1664, 1961.
DOI : 10.1103/PhysRev.124.1664

P. W. Anderson, Resonating valence bonds: A new kind of insulator?, Mat. Res. Bull, vol.8, issue.73, pp.15390167-15390167, 1973.

P. W. Anderson, The Resonating Valence Bond State in La2CuO4 and Superconductivity, Science, vol.235, issue.4793, p.1196, 1987.
DOI : 10.1126/science.235.4793.1196

P. Lecheminant, B. Bernu, C. Lhuillier, L. Pierre, and P. Sindzingre, lattice using exact spectra analysis, Physical Review B, vol.56, issue.5, p.2521, 1997.
DOI : 10.1103/PhysRevB.56.2521

G. Misguich, B. Bernu, C. Lhuillier, and C. Waldtmann, Spin Liquid in the Multiple-Spin Exchange Model on the Triangular Lattice: 3He on Graphite, Physical Review Letters, vol.81, issue.5, p.1098, 1998.
DOI : 10.1103/PhysRevLett.81.1098

G. Misguich, C. Lhuillier, B. Bernu, and C. Waldtmann, Spin-liquid phase of the multiple-spin exchange Hamiltonian on the triangular lattice, Physical Review B, vol.60, issue.2, 1999.
DOI : 10.1103/PhysRevB.60.1064

N. Read and S. Sachdev, expansion for frustrated quantum antiferromagnets, Physical Review Letters, vol.66, issue.13, p.1773, 1991.
DOI : 10.1103/PhysRevLett.66.1773

S. Sachdev, Kagome??- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons, Physical Review B, vol.45, issue.21, p.12377, 1992.
DOI : 10.1103/PhysRevB.45.12377

R. Moessner and S. L. Sondhi, Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model, Physical Review Letters, vol.86, issue.9, p.1881, 2001.
DOI : 10.1103/PhysRevLett.86.1881

A. Ralko, M. Ferrero, F. Becca, D. Ivanov, and F. Mila, Zero-temperature properties of the quantum dimer model on the triangular lattice, Physical Review B, vol.71, issue.22, p.224109, 2005.
DOI : 10.1103/PhysRevB.71.224109

A. Ralko, M. Ferrero, F. Becca, D. Ivanov, and F. Mila, Dynamics of the quantum dimer model on the triangular lattice: Soft modes and local resonating valence-bond correlations, Physical Review B, vol.74, issue.13, p.134301, 2006.
DOI : 10.1103/PhysRevB.74.134301

A. Ralko, M. Ferrero, F. Becca, D. Ivanov, and F. Mila, Crystallization of the resonating valence bond liquid as vortex condensation, Physical Review B, vol.76, issue.14, p.140404, 2007.
DOI : 10.1103/PhysRevB.76.140404

URL : https://hal.archives-ouvertes.fr/hal-00165804

P. Mendels, F. Bert, M. A. De-vries, A. Olariu, A. Harrison et al., Quantum Magnetism in the Paratacamite Family: Towards an Ideal Kagom?? Lattice, Physical Review Letters, vol.98, issue.7, p.77204, 2007.
DOI : 10.1103/PhysRevLett.98.077204

Y. Shimizu, K. Miyagawa, K. Kanoda, M. Maesato, and G. Saito, Spin Liquid State in an Organic Mott Insulator with a Triangular Lattice, Physical Review Letters, vol.91, issue.10, pp.10700110-1103, 2003.
DOI : 10.1103/PhysRevLett.91.107001

E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Ann. Phys, vol.16, issue.40761, pp.10-1016, 1961.

M. B. Hastings, Lieb-Schultz-Mattis in higher dimensions, Mattis in higher dimensions, p.104431, 2004.
DOI : 10.1103/PhysRevB.69.104431

M. Oshikawa, Commensurability, Excitation Gap, and Topology in Quantum Many-Particle Systems on a Periodic Lattice, Physical Review Letters, vol.84, issue.7, p.1535, 2000.
DOI : 10.1103/PhysRevLett.84.1535

X. G. Wen, Vacuum degeneracy of chiral spin states in compactified space, Physical Review B, vol.40, issue.10, 1989.
DOI : 10.1103/PhysRevB.40.7387

X. G. Wen, Mean-field theory of spin-liquid states with finite energy gap and topological orders, Physical Review B, vol.44, issue.6, p.2664, 1991.
DOI : 10.1103/PhysRevB.44.2664

S. Cheong and C. L. Henley, Correlation density matrix: An unbiased analysis of exact diagonalizations, Physical Review B, vol.79, issue.21, p.212402, 2009.
DOI : 10.1103/PhysRevB.79.212402

M. M. Wolf, F. Verstraete, M. B. Hastings, and J. I. Cirac, Area Laws in Quantum Systems: Mutual Information and Correlations, Physical Review Letters, vol.100, issue.7, pp.7050210-1103, 2008.
DOI : 10.1103/PhysRevLett.100.070502

M. A. Levin and X. Wen, String-net condensation:???A physical mechanism for topological phases, Physical Review B, vol.71, issue.4, p.45110, 2005.
DOI : 10.1103/PhysRevB.71.045110

G. Misguich, D. Serban, and V. Pasquier, Quantum Dimer Model on the Kagome Lattice: Solvable Dimer-Liquid and Ising Gauge Theory, Physical Review Letters, vol.89, issue.13, pp.13720210-1103, 2002.
DOI : 10.1103/PhysRevLett.89.137202

I. Affleck and A. W. Ludwig, Universal noninteger ??????ground-state degeneracy?????? in critical quantum systems, Physical Review Letters, vol.67, issue.2, p.161, 1991.
DOI : 10.1103/PhysRevLett.67.161

P. Fendley, R. Moessner, and S. L. Sondhi, Classical dimers on the triangular lattice, Physical Review B, vol.66, issue.21, p.214513, 2002.
DOI : 10.1103/PhysRevB.66.214513

A. Ioselevich, D. A. Ivanov, and M. V. Feigelman, Ground-state properties of the Rokhsar-Kivelson dimer model on the triangular lattice, Physical Review B, vol.66, issue.17, p.174405, 2002.
DOI : 10.1103/PhysRevB.66.174405

S. Furukawa, G. Misguich, and M. Oshikawa, Reduced density matrices and topological order in a quantum dimer model, Journal of Physics: Condensed Matter, vol.19, issue.14, pp.14521210-1088, 2007.
DOI : 10.1088/0953-8984/19/14/145212

M. Haque, O. Zozulya, and K. Schoutens, Entanglement Entropy in Fermionic Laughlin States, Physical Review Letters, vol.98, issue.6, p.60401, 2007.
DOI : 10.1103/PhysRevLett.98.060401

Y. Zhang, T. Grover, and A. Vishwanath, spin liquids and lattice Laughlin states, Physical Review B, vol.84, issue.7, p.75128, 2011.
DOI : 10.1103/PhysRevB.84.075128

M. Kac, Can One Hear the Shape of a Drum?, The American Mathematical Monthly, vol.73, issue.4, pp.10-2307, 1966.
DOI : 10.2307/2313748

R. G. Melko, A. B. Kallin, and M. B. Hastings, model, Physical Review B, vol.82, issue.10, p.100409, 2010.
DOI : 10.1103/PhysRevB.82.100409

R. R. Singh, M. B. Hastings, A. B. Kallin, and R. G. Melko, Finite-Temperature Critical Behavior of Mutual Information, Physical Review Letters, vol.106, issue.13, p.135701, 2011.
DOI : 10.1103/PhysRevLett.106.135701

J. Wilms, J. Vidal, F. Verstraete, and S. Dusuel, Finite-temperature mutual information in a simple phase transition, Journal of Statistical Mechanics: Theory and Experiment, vol.2012, issue.01, pp.102310-1088, 1023.
DOI : 10.1088/1742-5468/2012/01/P01023

J. Wilms, M. Troyer, and F. Verstraete, Mutual information in classical spin models, Journal of Statistical Mechanics: Theory and Experiment, vol.2011, issue.10, pp.1001110-1088, 2011.
DOI : 10.1088/1742-5468/2011/10/P10011

H. W. Lau and P. Grassberger, Information theoretic aspects of the two-dimensional Ising model, Physical Review E, vol.87, issue.2, p.22128, 2013.
DOI : 10.1103/PhysRevE.87.022128

J. Iaconis, S. Inglis, A. B. Kallin, and R. G. Melko, Detecting classical phase transitions with Renyi mutual information, doi:10.1103/PhysRevB, 2013.
DOI : 10.1103/PhysRevB.87.195134

A. Rahmani and G. Chern, Universal R??nyi mutual information in classical systems: The case of kagome ice, Physical Review B, vol.88, issue.5, p.54426, 2013.
DOI : 10.1103/PhysRevB.88.054426

H. W. Blote and H. J. Hilhorst, Roughening transitions and the zero-temperature triangular Ising antiferromagnet, Journal of Physics A: Mathematical and General, vol.15, issue.11, p.631, 1982.
DOI : 10.1088/0305-4470/15/11/011

F. Alet, Y. Ikhlef, J. L. Jacobsen, G. Misguich, and V. Pasquier, Classical dimers with aligning interactions on the square lattice, Physical Review E, vol.74, issue.4, p.41124, 2006.
DOI : 10.1103/PhysRevE.74.041124

URL : https://hal.archives-ouvertes.fr/hal-00115628

J. Stéphan, Shannon and Rényi mutual information in quantum critical spin chains, arXiv:1403, p.6157, 2014.

F. Alet, J. L. Jacobsen, G. Misguich, V. Pasquier, F. Mila et al., Interacting Classical Dimers on the Square Lattice, Physical Review Letters, vol.94, issue.23, pp.23570210-1103, 2005.
DOI : 10.1103/PhysRevLett.94.235702

URL : https://hal.archives-ouvertes.fr/hal-00005563

D. J. Luitz, N. Laflorencie, and F. Alet, Participation spectroscopy and entanglement Hamiltonian of quantum spin models, Journal of Statistical Mechanics: Theory and Experiment, vol.2014, issue.8, 2014.
DOI : 10.1088/1742-5468/2014/08/P08007

URL : https://hal.archives-ouvertes.fr/hal-00982470

F. Evers, A. D. Mirlin, and A. Transitions, Anderson transitions, Reviews of Modern Physics, vol.80, issue.4, p.1355, 2008.
DOI : 10.1103/RevModPhys.80.1355

Y. Y. Atas and E. Bogomolny, Multifractality of eigenfunctions in spin chains, Physical Review E, vol.86, issue.2, p.21104, 2012.
DOI : 10.1103/PhysRevE.86.021104

URL : https://hal.archives-ouvertes.fr/hal-00702547

M. P. Zaletel, J. H. Bardarson, and J. E. Moore, Logarithmic Terms in Entanglement Entropies of 2D Quantum Critical Points and Shannon Entropies of Spin Chains, Physical Review Letters, vol.107, issue.2, p.20402, 2011.
DOI : 10.1103/PhysRevLett.107.020402

F. C. Alcaraz and M. A. Rajabpour, Universal Behavior of the Shannon Mutual Information of Critical Quantum Chains, Physical Review Letters, vol.111, issue.1, p.17201, 2013.
DOI : 10.1103/PhysRevLett.111.017201

I. Affleck, Field Theory Methods and Quantum Critical Phenomena, Strings and Critical Phenomena, Proceedings of Les Houches Summer School, 1988.

P. Fendley, H. Saleur, and N. P. Warner, Exact solution of a massless scalar field with a relevant boundary interaction, Nuclear Physics B, vol.430, issue.3, pp.577-5960550, 1994.
DOI : 10.1016/0550-3213(94)90160-0

D. Schwandt, F. Alet, and M. Oshikawa, Valence bond distribution and correlation in bipartite Heisenberg antiferromagnets, Physical Review B, vol.89, issue.10, 2014.
DOI : 10.1103/PhysRevB.89.104416

URL : https://hal.archives-ouvertes.fr/hal-00982457

M. Oshikawa, Boundary Conformal Field Theory and Entanglement Entropy in Two- Dimensional Quantum Lifshitz Critical Point, 2010.

J. L. Cardy, Conformal invariance and surface critical behavior, Nuclear Physics B, vol.240, issue.4, pp.10-1016, 1984.
DOI : 10.1016/0550-3213(84)90241-4

C. G. Callan, I. R. Klebanov, A. W. Ludwig, and J. M. Maldacena, Exact solution of a boundary conformal field theory, Nuclear Physics B, vol.422, issue.3, pp.550-321390440, 1994.
DOI : 10.1016/0550-3213(94)90440-5

Y. Kumano, G. Misguich, and M. Oshikawa, Correlations and Luttinger parameter in the " Rényified " ground state of XXZ spin chains, 2014.

J. I. Cirac and G. Sierra, Infinite matrix product states, conformal field theory, and the Haldane-Shastry model, Physical Review B, vol.81, issue.10, p.104431, 2010.
DOI : 10.1103/PhysRevB.81.104431

J. Sawada, Generating Bracelets in Constant Amortized Time, SIAM Journal on Computing, vol.31, issue.1, pp.10-1137, 2001.
DOI : 10.1137/S0097539700377037

J. L. Cardy, Effect of boundary conditions on the operator content of two-dimensional conformally invariant theories, Nuclear Physics B, vol.275, issue.2, pp.10-1016, 1986.
DOI : 10.1016/0550-3213(86)90596-1

J. L. Cardy, Boundary conditions, fusion rules and the Verlinde formula, Nuclear Physics B, vol.324, issue.3, pp.58110-1016, 1989.
DOI : 10.1016/0550-3213(89)90521-X

M. Oshikawa and I. Affleck, Defect Lines in the Ising Model and Boundary States on Orbifolds, Physical Review Letters, vol.77, issue.13, p.2604, 1996.
DOI : 10.1103/PhysRevLett.77.2604

T. Wei and P. M. Goldbart, Geometric measure of entanglement and applications to bipartite and multipartite quantum states, Physical Review A, vol.68, issue.4, p.42307, 2003.
DOI : 10.1103/PhysRevA.68.042307

T. Wei, D. Das, S. Mukhopadyay, S. Vishveshwara, and P. M. Goldbart, Global entanglement and quantum criticality in spin chains, Physical Review A, vol.71, issue.6, p.60305, 2005.
DOI : 10.1103/PhysRevA.71.060305

Q. Shi, R. Orús, J. O. Fjaerestad, and H. Zhou, Finite-size geometric entanglement from tensor network algorithms, New Journal of Physics, vol.12, issue.2, pp.250081367-2630, 2010.
DOI : 10.1088/1367-2630/12/2/025008

H. F. Song, N. Laflorencie, S. Rachel, and K. L. Hur, Entanglement entropy of the two-dimensional Heisenberg antiferromagnet, Physical Review B, vol.83, issue.22, p.224410, 2011.
DOI : 10.1103/PhysRevB.83.224410

A. B. Kallin, M. B. Hastings, R. G. Melko, and R. R. Singh, Anomalies in the entanglement properties of the square-lattice Heisenberg model, Physical Review B, vol.84, issue.16, p.165134, 2011.
DOI : 10.1103/PhysRevB.84.165134

D. J. Luitz, F. Alet, and N. Laflorencie, criticality, Physical Review B, vol.89, issue.16, p.165106, 2014.
DOI : 10.1103/PhysRevB.89.165106

URL : https://hal.archives-ouvertes.fr/hal-00982461

B. Duplantier and F. David, Exact partition functions and correlation functions of multiple Hamiltonian walks on the Manhattan lattice, J. Stat. Phys, vol.51, issue.327, pp.10-1007, 1988.

B. Osgood, R. Phillips, and P. Sarnak, Extremals of determinants of Laplacians, Journal of Functional Analysis, vol.80, issue.1, pp.10-1016, 1988.
DOI : 10.1016/0022-1236(88)90070-5

P. W. Anderson, An Approximate Quantum Theory of the Antiferromagnetic Ground State, Phys. Rev, vol.86, issue.694, 1952.

B. Bernu, C. Lhuillier, and L. Pierre, Signature of N??el order in exact spectra of quantum antiferromagnets on finite lattices, Physical Review Letters, vol.69, issue.17, p.2590, 1992.
DOI : 10.1103/PhysRevLett.69.2590

C. Lhuillier, Frustrated Quantum Magnets, p.502464, 2005.
DOI : 10.1007/3-540-45649-X_6

E. Lieb and D. Mattis, Ordering Energy Levels of Interacting Spin Systems, Journal of Mathematical Physics, vol.3, issue.4, p.749, 1962.
DOI : 10.1063/1.1724276