Information measures for a local quantum phase transition: Lattice fermions in a one-dimensional harmonic trap

Abstract

We use quantum information measures to study the local quantum phase transition that occurs for trapped spinless fermions in one-dimensional lattices. We focus on the case of a harmonic confinement. The transition occurs upon increasing the characteristic density and results in the formation of a band-insulating domain in the center of the trap. We show that the ground-state bipartite entanglement entropy can be used as an order parameter to characterize this local quantum phase transition. We also study excited eigenstates by calculating the average von Neumann and second Renyi eigenstate entanglement entropies, and compare the results with the thermodynamic entropy and the mutual information of thermal states at the same energy density. While at low temperatures we observe a linear increase of the thermodynamic entropy with temperature at all characteristic densities, the average eigenstate entanglement entropies exhibit a strikingly different behavior as functions of temperature below and above the transition. They are linear in temperature below the transition but exhibit activated behavior above it. Hence, at nonvanishing energy densities above the ground state, the average eigenstate entanglement entropies carry fingerprints of the local quantum phase transition.

11 pages, 10 figures, Editor's Suggestion

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Cited by in corpus (14)

• Entanglement and matrix elements of observables in interacting integrable systems
• Operationally accessible entanglement of one dimensional spinless fermions
• Volume Law and Quantum Criticality in the Entanglement Entropy of Excited Eigenstates of the Quantum Ising Model
• Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models
• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
• Bipartite entanglement entropy of the excited states of the free fermions and the harmonic oscillators
• Entanglement and relative entropies for low-lying excited states in inhomogeneous one-dimensional quantum systems
• Tight-binding billiards
• Engineering entanglement Hamiltonians with strongly interacting cold atoms in optical traps
• Typical entanglement entropy in systems with particle-number conservation
• Information measures for a local quantum phase transition: Lattice bosons in a one-dimensional harmonic trap
• Entanglement as a topological marker in harmonically confined attractive Fermi-Hubbard chains
• Volume-law entanglement entropy of typical pure quantum states