Fluctuations in subsystems of the zero temperature XX chain: Emergence of an effective temperature

Abstract

The zero-temperature XX chain is studied with emphasis on the properties of a block of $L$ spins inside the chain. We investigate the quantum fluctuations resulting from the entanglement of the block with the rest of the chain using analytical as well as numerical (density matrix renormalization group) methods. It is found that the rest of the chain acts as a thermal environment and an effective temperature can be introduced to describe the fluctuations. We show that the effective temperature description is robust in the sense that several independent definitions (through fluctuation dissipation theorem, comparing with a finite temperature system) yield the same functional form in the limit of large block size ($L\to \infty$). The effective temperature can also be shown to satisfy the basic requirements on how it changes when two bodies of equal or unequal temperatures are brought into contact.

arXiv comment19 pages, 7 figures

References in corpus (15)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Calculation of reduced density matrices from correlation functions
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Density-Matrix Spectra of Solvable Fermionic Systems
• Quantum data compression, quantum information generation, and the density-matrix renormalization group method
• Random Matrix Theory and Entanglement in Quantum Spin Chains
• Density-matrix spectra for integrable models
• On Density-Matrix Spectra for Two-Dimensional Quantum Systems
• Density Matrices for a Chain of Oscillators
• Isotropic Transverse XY Chain with Energy- and Magnetization Currents
• Entanglement in the XX spin chain with an energy current
• Entanglement and majorization in (1+1)-dimensional quantum systems
• Operator-Based Truncation Scheme Based on the Many-Body Fermion Density Matrix

Cited by in corpus (21)

• Quantum entanglement in condensed matter systems
• Reduced density matrices and entanglement entropy in free lattice models
• The effective temperature
• Evolution of entanglement after a local quench
• General Relation between Entanglement and Fluctuations in One Dimension
• Exact relations between particle fluctuations and entanglement in Fermi gases
• On the relation between entanglement and subsystem Hamiltonians
• Entanglement and particle correlations of Fermi gases in harmonic traps
• Magnetization and entanglement after a geometric quench in the XXZ chain
• Fluctuations and Entanglement spectrum in quantum Hall states
• The von Neumann entropy asymptotics in multidimensional fermionic systems
• Surface and bulk entanglement in free-fermion chains
• Fano resonances and entanglement entropy
• Entanglement Spectra and Entanglement Thermodynamics of Hofstadter Bilayers
• Thermalization by a synthetic horizon
• Boiling Quantum Vacuum: Thermal Subsystems from Ground-State Entanglement
• Some speculations about local thermalization of nonequilibrium extended quantum systems
• Entanglement-fluctuation relation for bipartite pure states
• Projective approach to the entanglement entropy of 1-$d$ fermions
• Domain-wall melting and entanglement in free-fermion chains with a band structure
• Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study