Information measures for local quantum phase transitions: Lattice bosons in a one-dimensional harmonic trap

Yicheng Zhang, Lev Vidmar, Marcos Rigol

Research output: Contribution to journalArticle

Abstract

We study ground-state quantum entanglement in the one-dimensional Bose-Hubbard model in the presence of a harmonic trap. We focus on two transitions that occur upon increasing the characteristic particle density: The formation of a Mott-insulating domain with site occupation one at the center of the trap (lower transition) and the emergence of a superfluid domain at the center of the Mott-insulating one (upper transition). These transitions generate discontinuities in derivatives of the total energy and have been characterized by local (nonextensive) order parameters, so we refer to them as local quantum phase transitions. We show that a second derivative of the total energy is continuous with a kink at the lower transition, and that it is discontinuous at the upper transition. We also show that bipartite entanglement entropies are order parameters for those local quantum phase transitions. We use the density-matrix renormalization group and show that the transition points extracted from entanglement measures agree with the predictions of the local density approximation in the thermodynamic limit. We discuss how to determine the transition points from results in small systems, such as the ones realized in recent optical lattice experiments that measured the second-order Renyi entanglement entropy.

Original languageEnglish (US)
Article number053611
JournalPhysical Review A
Volume100
Issue number5
DOIs
StatePublished - Nov 13 2019

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bosons
traps
harmonics
transition points
entropy
occupation
discontinuity
thermodynamics
ground state
energy
predictions
approximation

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

Cite this

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abstract = "We study ground-state quantum entanglement in the one-dimensional Bose-Hubbard model in the presence of a harmonic trap. We focus on two transitions that occur upon increasing the characteristic particle density: The formation of a Mott-insulating domain with site occupation one at the center of the trap (lower transition) and the emergence of a superfluid domain at the center of the Mott-insulating one (upper transition). These transitions generate discontinuities in derivatives of the total energy and have been characterized by local (nonextensive) order parameters, so we refer to them as local quantum phase transitions. We show that a second derivative of the total energy is continuous with a kink at the lower transition, and that it is discontinuous at the upper transition. We also show that bipartite entanglement entropies are order parameters for those local quantum phase transitions. We use the density-matrix renormalization group and show that the transition points extracted from entanglement measures agree with the predictions of the local density approximation in the thermodynamic limit. We discuss how to determine the transition points from results in small systems, such as the ones realized in recent optical lattice experiments that measured the second-order Renyi entanglement entropy.",
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Information measures for local quantum phase transitions : Lattice bosons in a one-dimensional harmonic trap. / Zhang, Yicheng; Vidmar, Lev; Rigol, Marcos.

In: Physical Review A, Vol. 100, No. 5, 053611, 13.11.2019.

Research output: Contribution to journalArticle

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