Entanglement Thermodynamics

Abstract

We investigate further the relationship between the entanglement spectrum of a composite many-body system and the energy spectrum of a subsystem making use of concepts of canonical thermodynamics. In many important cases the entanglement Hamiltonian is, in the limit of strong coupling between subsystems, proportional to the energy Hamiltonian of the subsystem. The proportionality factor is an appropriately defined coupling parameter, suggesting to interpret the latter as a inverse temperature. We identify a condition on the entanglement Hamiltonian which rigorously guarantees this interpretation to hold and removes any ambiguity in the definition of the entanglement Hamiltonian regarding contributions proportional to the unit operator. Illustrations of our findings are provided by spin ladders of arbitrary spin length, and by bilayer quantum Hall systems at total filling factor nu=2. Within mean-field description, the latter system realizes an entanglement spectrum of free fermions with just two levels of equal modulus where the analogies to canonical thermodynamics are particularly close.

13 pages, 1 figure. Invited contribution to JSTAT Special Issue: Quantum Entanglement in Condensed Matter Physics, version as published

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Cited by in corpus (34)

• Quantum entanglement in condensed matter systems
• Gravitational Dynamics From Entanglement "Thermodynamics"
• Thermodynamical Property of Entanglement Entropy for Excited States
• Entanglement Temperature and Entanglement Entropy of Excited States
• Dynamics of Entanglement Entropy from Einstein Equation
• Dynamical entanglement entropy with angular momentum and U(1) charge
• Entanglement Hamiltonian of Interacting Fermionic Models
• Bound states and entanglement in the excited states of quantum spin chains
• On the Time Evolution of Holographic n-partite Information
• Trigonal Warping in Bilayer Graphene: Energy versus Entanglement Spectrum
• Very General Holographic Superconductors and Entanglement Thermodynamics
• Entanglement in macroscopic systems
• Entanglement Hamiltonians and entropy in 1+1D chiral fermion systems
• Entanglement thermodynamics for charged black holes
• Entanglement spectrum and number fluctuations in the spin-partitioned BCS ground state
• Capacity of entanglement and distribution of density matrix eigenvalues in gapless systems
• Holographic entanglement first law for d + 1 dimensional rotating cylindrical black holes
• Entanglement Thermodynamics of the Generalized Charged BTZ Black Hole
• Momentum-Space Entanglement in Heisenberg Spin-Half Ladders
• Comments on universal properties of entanglement entropy and bulk reconstruction
• Holographic entanglement thermodynamics for higher dimensional charged black hole
• Holographic Entanglement Entropy, Subregion Complexity and Fisher Information metric of `black' Non-SUSY D3 Brane
• Entanglement entropy at higher orders for the states of a = 3 θ = 1 Lifshitz theory
• On a lightlike limit of entanglement
• Entanglement spectrum of fermionic bilayer honeycomb lattice: Hofstadter butterfly
• Initial-state-dependent thermalization in open qubits
• Intercomponent entanglement entropy and spectrum in binary Bose-Einstein condensates
• Holographic entanglement entropy of the double Wick rotated BTZ black hole
• Entanglement temperature for black branes with hyperscaling violation
• A perturbative study on the analytic continuation for generalized gravitational entropy
• Entanglement of Free Fermions and Bosons at Finite Temperature
• Derivation of Bose-Einstein and Fermi-Dirac statistics from quantum mechanics: gauge-theoretical structure
• Entanglement spectra of superconductivity ground states on the honeycomb lattice
• Effective thermodynamics of isolated entangled squeezed and coherent states