Estimating Quasi-long-range Order via Renyi Entropies

Abstract

We show how entanglement entropies allow for the estimation of quasi-long-range order in one dimensional systems whose low-energy physics is well captured by the Tomonaga-Luttinger liquid universality class. First, we check our procedure in the exactly solvable XXZ spin-1/2 chain in its entire critical region, finding very good agreement with Bethe ansatz results. Then, we show how phase transitions between different dominant orders may be efficiently estimated by considering the superfluid-charge density wave transition in a system of dipolar bosons. Finally, we discuss the application of this method to multispecies systems such as the one dimensional Hubbard model. Our work represent the first proof of a direct relationship between the Luttinger parameter and Rényi entropies in both bosonics and fermionic lattice models.

v2: minimal changes, 6 pages, 7 figures, accepted for publication in Phys. Rev. B

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• Symmetry resolved entanglement entropy of excited states in a CFT
• Random matrices and entanglement entropy of trapped Fermi gases
• Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition
• Entanglement Hamiltonians of lattice models via the Bisognano-Wichmann theorem
• Towards entanglement negativity of two disjoint intervals for a one dimensional free fermion
• Entanglement Entropies in Conformal Systems with Boundaries
• Spin structures and entanglement of two disjoint intervals in conformal field theories
• Tomonaga-Luttinger-liquid criticality: numerical entanglement entropy approach
• The entanglement entropy of 1D systems in continuous and homogenous space
• Genuine Multipartite Entanglement in the $XY$ Model
• Shell-Filling Effect in the Entanglement Entropies of Spinful Fermions
• Finite-size corrections of the Entanglement Entropy of critical quantum chains
• Universal aspects in the behavior of the entanglement spectrum in one dimension: scaling transition at the factorization point and ordered entangled structures
• Entanglement Hamiltonian of quantum critical chains and conformal field theories
• Gap scaling at Berezinskii-Kosterlitz-Thouless quantum critical points in one-dimensional Hubbard and Heisenberg models
• Entanglement and relative entropies for low-lying excited states in inhomogeneous one-dimensional quantum systems
• Entanglement evolution across defects in critical anisotropic Heisenberg chains
• Renyi entanglement entropies of descendant states in critical systems with boundaries: conformal field theory and spin chains
• Entanglement and corner Hamiltonian spectra of integrable open spin chains
• Critical properties and Rényi entropies of the spin-3/2 XXZ chain
• Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law
• Renormalization group flows for Wilson-Hubbard matter and the topological Hamiltonian
• Entanglement in low-energy states of the random-hopping model
• Measuring von Neumann entanglement entropies without wave functions
• Correlation Length and Unusual Corrections to the Entanglement Entropy
• Discrete Symmetry Breaking Transitions Between Paired Superfluids
• Entanglement Entropies of the quarter filled Hubbard model
• Oscillating terms in the Renyi entropy of Fermi liquids
• Estimating the central charge from the Rényi entanglement entropy
• Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions
• Rényi entanglement entropy of critical SU($N$) spin chains
• Spontaneous Peierls dimerization and emergent bond order in one-dimensional dipolar gases
• Spatial entanglement entropy in the ground state of the Lieb-Liniger model
• Klein bottle entropy of compactified boson conformal field theory
• Finite Size Scaling of Topological Entanglement Entropy
• Entanglement and boundary entropy in quantum spin chains with arbitrary direction of the boundary magnetic fields
• An efficient Monte Carlo algorithm for the evaluation of Renyi entanglement entropy of a general quantum dimer model at the R-K point
• Phase diagram study of a dimerized spin-S zig-zag ladder
• Quantum Correlations in Field Theory and Integrable Systems
• Unusual Corrections to the Scaling of the Entanglement Entropy of the Excited states in Conformal Field Theory