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

References in corpus (8)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement Spectrum and Entanglement Thermodynamics of Quantum Hall Bilayers at nu=1
• Entanglement Entropy and Spectra of the One-dimensional Kugel-Khomskii Model
• NMR Evidence for Spin Canting in a Bilayer nu = 2 Quantum Hall System
• Entanglement Spectra of Heisenberg Ladders of higher Spin
• Magnetotransport Study of the Canted Antiferromagnetic Phase in Bilayer $\nu =2$ Quantum Hall State
• The Study of Goldstone Modes in $\nu$=2 Bilayer Quantum Hall Systems
• Spin Supercurrent in the Canted Antiferromagnetic Phase

Cited by in corpus (6)

• Thermodynamical Property of Entanglement Entropy for Excited States
• Bound states and entanglement in the excited states of quantum spin chains
• Very General Holographic Superconductors and Entanglement Thermodynamics
• Entanglement spectrum and number fluctuations in the spin-partitioned BCS ground state
• On a lightlike limit of entanglement
• A perturbative study on the analytic continuation for generalized gravitational entropy