Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1212.5634 · Physical Review Letters

Entanglement Spectrum of the Two-Dimensional Bose-Hubbard Model

Vincenzo Alba, Masudul Haque, Andreas Martin Läuchli

Published Jun 26, 2013• 88 citations
arXivHTMLPDF

Abstract

We study the entanglement spectrum (ES) of the Bose-Hubbard model on the two-dimensional square lattice at unit filling, both in the Mott insulating and in the superfluid phase. In the Mott phase, we demonstrate that the ES is dominated by the physics at the boundary between the two subsystems. On top of the boundary-local (perturbative) structure, the ES exhibits substructures arising from one-dimensional dispersions along the boundary. In the superfluid phase, the structure of the ES is qualitatively different, and reflects the spontaneously broken U(1) symmetry of the phase. We attribute the basic low-lying structure to the "tower of states" Hamiltonian of the model. We then discuss how these characteristic structures evolve across the superfluid to Mott insulator transition and their influence on the behavior of the entanglement entropies. We briefly outline the implications of the ES structure on the efficiency of matrix-product-state based algorithms in two dimensions.

DOI
10.1103/physrevlett.110.260403

Related papers

Entanglement Entropy across the Superfluid-Insulator Transition: A Signature of Bosonic Criticality

Irénée Frérot, Tommaso Roscilde

We study the entanglement entropy and entanglement spectrum of the paradigmatic Bose-Hubbard model, describing strongly correlated bosons on a lattice. The use of a controlled approximation-the slave-boson approach-allows us to study entanglement in all regimes of the model (and, most importantly, across its superfluid-Mott-insulator transition) at a minimal cost. We find that the area-law scaling of entanglement-verified in all the phases-exhibits a sharp singularity at the transition. The singularity is greatly enhanced when the transition is crossed at fixed, integer filling, due to a richer entanglement spectrum containing an additional gapless mode, which descends from the amplitude (Higgs) mode of the global excitation spectrum-while this mode remains gapped at the generic (commensurate-incommensurate) transition with variable filling. Hence, the entanglement properties contain a unique signature of the two different forms of bosonic criticality exhibited by the Bose-Hubbard model.

arXiv:1512.00805•Physical Review Letters•May 11, 2016•70 citations

Entanglement Properties of the One-Dimensional Dimerized Fermi-Hubbard Model

Min-Chul Cha, Hoon Beom Kwon, JI-Woo Lee +1 more

We study the entanglement properties of the one-dimensional dimerized Fermi-Hubbard model. Using a matrix-product-state approach, we compute the ground state and identify two insulating phases at 1/2- and 3/4-filling, along with a metallic phase, whose mechanisms can be characterized by their entanglement spectra. Our findings indicate that the two insulating phases are distinct, implying that the phase at 1/2-filling has a charge gap arising from the band gap, which is enhanced by repulsive interactions, while the phase at 3/4-filling exhibits a Mott gap resulting from particle interactions. This difference between the two insulating phases is reflected in the scaling properties of the half-chain entanglement entropy and the distribution of the entanglement spectrum.

arXiv:2602.20990•Feb 24, 2026•0 citations

Spectral and Entanglement Properties of the Bosonic Haldane Insulator

Satoshi Ejima, Florian Lange, Holger Fehske

We discuss the existence of a nontrivial topological phase in one-dimensional interacting systems described by the extended Bose-Hubbard model with a mean filling of one boson per site. Performing large-scale density-matrix renormalization group calculations we show that the presence of nearest-neighbor repulsion enriches the ground-state phase diagram of the paradigmatic Bose-Hubbard model by stabilizing a novel gapped insulating state, the so-called Haldane insulator, which, embedded into superfluid, Mott insulator, and density wave phases, is protected by the lattice inversion symmetry. The quantum phase transitions between the different insulating phases were determined from the central charge via the von Neumann entropy. The Haldane phase reveals a characteristic fourfold degeneracy of the entanglement spectrum. We finally demonstrate that the intensity maximum of the dynamical charge structure factor, accessible by Bragg spectroscopy, features the gapped dispersion known from the spin-1 Heisenberg chain.

arXiv:1407.2852•Physical Review Letters•Jul 8, 2014•48 citations

Quantum phase transitions in the matrix product states of the one-dimensional boson Hubbard model

Min-Chul Cha

We study quantum phase transitions in the matrix product states of the one-dimensional boson Hubbard model, whose amount of entanglement is limited by the size of the matrices used in the representation of the states. By measuring entanglement entropy and other physical properties, we observe that the Mott-insulator-to-superfluid transitions occur sharp and continuous, accompanied by shifting transition points that are not blurred by finite entanglement effects. This strongly suggests that the transition always occurs between the Mott insulator and a mean-field-like compressible state, followed by the more entangled superfluid state. Both $O(2)$ and the commensurate-incommensurate transitions are studied, whose properties can be characterized by entanglement spectra and critical exponents.

Physical review. B./Physical review. B•Dec 14, 2022•2 citations

Entanglement spectrum of one-dimensional extended Bose-Hubbard models

Xiaolong Deng, Luis Santos

The entanglement spectrum provides crucial information about correlated quantum systems. We show that the study of the blocklike nature of the reduced density matrix in number sectors and the partition dependence of the spectrum in finite systems leads to interesting unexpected insights, which we illustrate for the case of a one-dimensional extended Hubbard model. We show that block symmetry provides an intuitive understanding of the spectral double degeneracy of the Haldane insulator, which is remarkably maintained at low on-site interaction, where triple or higher site occupation is significant and particle-hole symmetry is broken. Moreover, surprisingly, the partition dependence of the spectral degeneracy in the Haldane insulator, and of a partial degeneracy in the Mott insulator, is directly linked to the, in principle unrelated, density-density correlations, and presents an intriguing periodic behavior in superfluid and supersolid phases.

arXiv:1104.5157•Physical Review B•Aug 30, 2011•67 citations

Quantum critical behavior of ultracold bosons in the two-dimensional Bose-Hubbard lattice

Ulli Pohl, Sayak Ray, Johann Kroha

We investigate the temperature-dependent behavior emerging in the vicinity of the superfluid (SF) to Mott insulator (MI) transition of interacting bosons in a two-dimensional optical lattice, described by the Bose-Hubbard model. The equilibrium phase diagram at finite temperatures is computed by means of the cluster mean-field theory (CMF) where the effect of non-local correlations is analyzed systematically by finite-size scaling of the cluster size. The phase diagram exhibits a rich structure including a transition and a crossover of the SF and MI phases respectively to a normal fluid (NF) state at finite temperature. In order to characterize these phases, and the NF transition and crossover scales, we calculate, in addition to the condensate amplitude, the superfluid fraction, sound velocity and compressibility. The phase boundaries obtained by CMF with finite-size scaling agree quantitatively with quantum Monte Carlo (QMC) results as well as with experiments. The von Neumann entanglement entropy of a cluster exhibits critical enhancement near the SF-MI quantum critical point (QCP). We also discuss the behavior of the transition lines near this QCP at the particle-hole symmetric point located at the tip of a Mott lobe as well as away from particle-hole symmetry.

•Jun 28, 2021•0 citations
We study the entanglement spectrum (ES) of the Bose-Hubbard model on the two-dimensional square lattice at unit filling, both in the Mott insulating and in the superfluid phase. In the Mott phase, we demonstrate that the ES is dominated by the physics at the boundary between the two subsystems. On top of the boundary-local (perturbative) structure, the ES exhibits substructures arising from one-dimensional dispersions along the boundary. In the superfluid phase, the structure of the ES is qualitatively different, and reflects the spontaneously broken U(1) symmetry of the phase. We attribute the basic low-lying structure to the "tower of states" Hamiltonian of the model. We then discuss how these characteristic structures evolve across the superfluid to Mott insulator transition and their influence on the behavior of the entanglement entropies. We briefly outline the implications of the ES structure on the efficiency of matrix-product-state based algorithms in two dimensions.
We study the entanglement entropy and entanglement spectrum of the paradigmatic Bose-Hubbard model, describing strongly correlated bosons on a lattice. The use of a controlled approximation-the slave-boson approach-allows us to study entanglement in all regimes of the model (and, most importantly, across its superfluid-Mott-insulator transition) at a minimal cost. We find that the area-law scaling of entanglement-verified in all the phases-exhibits a sharp singularity at the transition. The singularity is greatly enhanced when the transition is crossed at fixed, integer filling, due to a richer entanglement spectrum containing an additional gapless mode, which descends from the amplitude (Higgs) mode of the global excitation spectrum-while this mode remains gapped at the generic (commensurate-incommensurate) transition with variable filling. Hence, the entanglement properties contain a unique signature of the two different forms of bosonic criticality exhibited by the Bose-Hubbard model.
We study the entanglement properties of the one-dimensional dimerized Fermi-Hubbard model. Using a matrix-product-state approach, we compute the ground state and identify two insulating phases at 1/2- and 3/4-filling, along with a metallic phase, whose mechanisms can be characterized by their entanglement spectra. Our findings indicate that the two insulating phases are distinct, implying that the phase at 1/2-filling has a charge gap arising from the band gap, which is enhanced by repulsive interactions, while the phase at 3/4-filling exhibits a Mott gap resulting from particle interactions. This difference between the two insulating phases is reflected in the scaling properties of the half-chain entanglement entropy and the distribution of the entanglement spectrum.
We discuss the existence of a nontrivial topological phase in one-dimensional interacting systems described by the extended Bose-Hubbard model with a mean filling of one boson per site. Performing large-scale density-matrix renormalization group calculations we show that the presence of nearest-neighbor repulsion enriches the ground-state phase diagram of the paradigmatic Bose-Hubbard model by stabilizing a novel gapped insulating state, the so-called Haldane insulator, which, embedded into superfluid, Mott insulator, and density wave phases, is protected by the lattice inversion symmetry. The quantum phase transitions between the different insulating phases were determined from the central charge via the von Neumann entropy. The Haldane phase reveals a characteristic fourfold degeneracy of the entanglement spectrum. We finally demonstrate that the intensity maximum of the dynamical charge structure factor, accessible by Bragg spectroscopy, features the gapped dispersion known from the spin-1 Heisenberg chain.
We study quantum phase transitions in the matrix product states of the one-dimensional boson Hubbard model, whose amount of entanglement is limited by the size of the matrices used in the representation of the states. By measuring entanglement entropy and other physical properties, we observe that the Mott-insulator-to-superfluid transitions occur sharp and continuous, accompanied by shifting transition points that are not blurred by finite entanglement effects. This strongly suggests that the transition always occurs between the Mott insulator and a mean-field-like compressible state, followed by the more entangled superfluid state. Both O(2)O(2)O(2) and the commensurate-incommensurate transitions are studied, whose properties can be characterized by entanglement spectra and critical exponents.
The entanglement spectrum provides crucial information about correlated quantum systems. We show that the study of the blocklike nature of the reduced density matrix in number sectors and the partition dependence of the spectrum in finite systems leads to interesting unexpected insights, which we illustrate for the case of a one-dimensional extended Hubbard model. We show that block symmetry provides an intuitive understanding of the spectral double degeneracy of the Haldane insulator, which is remarkably maintained at low on-site interaction, where triple or higher site occupation is significant and particle-hole symmetry is broken. Moreover, surprisingly, the partition dependence of the spectral degeneracy in the Haldane insulator, and of a partial degeneracy in the Mott insulator, is directly linked to the, in principle unrelated, density-density correlations, and presents an intriguing periodic behavior in superfluid and supersolid phases.
We investigate the temperature-dependent behavior emerging in the vicinity of the superfluid (SF) to Mott insulator (MI) transition of interacting bosons in a two-dimensional optical lattice, described by the Bose-Hubbard model. The equilibrium phase diagram at finite temperatures is computed by means of the cluster mean-field theory (CMF) where the effect of non-local correlations is analyzed systematically by finite-size scaling of the cluster size. The phase diagram exhibits a rich structure including a transition and a crossover of the SF and MI phases respectively to a normal fluid (NF) state at finite temperature. In order to characterize these phases, and the NF transition and crossover scales, we calculate, in addition to the condensate amplitude, the superfluid fraction, sound velocity and compressibility. The phase boundaries obtained by CMF with finite-size scaling agree quantitatively with quantum Monte Carlo (QMC) results as well as with experiments. The von Neumann entanglement entropy of a cluster exhibits critical enhancement near the SF-MI quantum critical point (QCP). We also discuss the behavior of the transition lines near this QCP at the particle-hole symmetric point located at the tip of a Mott lobe as well as away from particle-hole symmetry.