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:2002.10602 · Physical review. B./Physical review. B

Quantum phase transition of the Bose-Hubbard model with anisotropic hopping on a cubic lattice

Tao Wang, Xue‐Feng Zhang

Published Jul 30, 2020• 1 citation
arXivHTMLPDF

Abstract

In a quantum many-body system, dimensionality plays a critical role in determining the type of quantum phase transition. To study the quantum system during dimensional crossover, we studied the Bose-Hubbard model on a cubic lattice with anisotropic hopping by using the high-order symbolic strong-coupling expansion method. The analytic series expanded boundaries between the Mott insulator and the superfluid phase up to eighth order are calculated. The critical exponents are extracted by the Pad\'e resummation method, which clearly shows dimensional crossover behavior. Meanwhile, the critical points at commensurate filling can also be obtained, and they match well with the prediction of renormalization group theory. Finally, the scaling of the gap energy and the whole phase diagram are given, and they can be taken as the benchmark for experiment and numerical simulations in future study.

DOI
10.1103/physrevb.102.024522

Related papers

High-order strong-coupling expansion for the Bose-Hubbard model

Tao Wang, Xuefeng Zhang, Chunfeng Hou +2 more

Based on the process-chain method, we work out in detail a high-order strong-coupling expansion (HSCE) algorithm for determining the quantum phase boundary between the Mott insulator and the superfluid phase of the Bose-Hubbard model in different dimensions. A comparison with quantum Monte-Carlo results reveals the high efficiency and accuracy of the HSCE. With a symbolized evaluation of the algorithm we obtain an analytic expression for the strong-coupling boundary for different fillings up to eighth order. A subsequent Pad\'e approximation then yields a scaling function, which rescales lobes with different fillings to one lobe. As a further crosscheck, we perform a hopping expansion of the phase boundaries obtained from the effective potential Landau theory (EPLT) and find that the respective expansion coefficients coincide with those of HSCE.

•Jan 5, 2018•2 citations

High-order symbolic strong-coupling expansion for the Bose-Hubbard model

Tao Wang, Xue‐Feng Zhang, Chunfeng Hou +2 more

Combining the process-chain method with a symbolized evaluation, we work out in detail a high-order symbolic strong-coupling expansion (HSSCE) for determining the quantum phase boundaries between the Mott insulator and the superfluid phase of the Bose-Hubbard model for different fillings in hypercubic lattices of different dimensions. With a subsequent Pad\'e approximation we achieve for the quantum phase boundaries a high accuracy, which is comparable to high-precision quantum Monte-Carlo simulations, and show that all the Mott lobes can be rescaled to a single one. As a further cross-check, we find that the HSSCE results coincide with a hopping expansion of the quantum phase boundaries, which follow from the effective potential Landau theory.

arXiv:1801.01862•Physical review. B./Physical review. B•Dec 4, 2018•14 citations

Ground-state phase diagram of the two-dimensional Bose-Hubbard model with anisotropic hopping

Janik Schönmeier-Kromer, Lode Pollet

We compute the ground-state phase diagram of the two-dimensional (2D) Bose-Hubbard model with anisotropic hopping using quantum Monte Carlo simulations, connecting the one-dimensional (1D) to the 2D system. We find that the tip of the lobe lies on a curve controlled by the 1D limit over the full anisotropy range, while the universality class is always the same as in the isotropic 2D system. This behavior can be derived analytically from the lowest renormalization-group equations and has a shape typical for the underlying Kosterlitz-Thouless transition in one dimension. We also compute the phase boundary of the Mott lobe at unit density for strong anisotropy and compare it to the 1D system. Our calculations shed light on recent cold gas experiments monitoring the dynamics of an expanding cloud.

arXiv:1308.2229•Physical Review A•Feb 7, 2014•16 citations

Strong-coupling expansion for the two-species Bose-Hubbard model

M. Iskin

To analyze the ground-state phase diagram of Bose-Bose mixtures loaded into $d$-dimensional hypercubic optical lattices, we perform a strong-coupling power-series expansion in the kinetic energy term (plus a scaling analysis) for the two-species Bose-Hubbard model with onsite boson-boson interactions. We consider both repulsive and attractive interspecies interaction, and obtain an analytical expression for the phase boundary between the incompressible Mott insulator and the compressible superfluid phase up to third order in the hoppings. In particular, we find a re-entrant quantum phase transition from paired superfluid (superfluidity of composite bosons, i.e., Bose-Bose pairs) to Mott insulator and again to a paired superfluid in all one, two, and three dimensions, when the interspecies interaction is sufficiently large and attractive. We hope that some of our results could be tested with ultracold atomic systems.

arXiv:1001.0021•Physical Review A•Sep 30, 2010•30 citations

Bose-Hubbard Model with Power-Law Hopping in One Dimension

Tanul Gupta, Nikolay V. Prokof'ev, Guido Pupillo

We investigate the zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with power-law hopping decaying with distance as 1/r^{α} using exact large scale quantum Monte Carlo simulations. For all 1<α≤3 the quantum phase transition from a superfluid and a Mott insulator at unit filling is found to be continuous and scale invariant, in marked contrast with the Berezinskii-Kosterlitz-Thouless (BKT) scenario that is recovered only for α>3. By performing finite-size scaling collapses of the superfluid stiffness and extracting dynamical and correlation-length exponents from the low-energy spectrum, we establish that these transitions define a distinct universality class throughout the long-range regime 1<α≤3. Analysis of the single-particle correlation functions and grand canonical phase diagram further reveals a sequence of ordering regimes within the superfluid phase: true long-range order for α≤2, anomalous quasi-long-range order for 2<α≤3, and conventional algebraic decay for α>3. Our exact numerical results provide a benchmark to compare theories of long-range quantum models and are relevant for experiments with cold neutral atom, molecules and ion chains.

arXiv:2412.01571•Physical Review Letters•Apr 15, 2026•2 citations

Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid-to-Mott-insulator transition in the one-dimensional Bose-Hubbard model

Juan Carrasquilla, Salvatore R. Manmana, Marcos Rigol

We investigate the interaction-induced superfluid-to-Mott-insulator transition in the one-dimensional Bose-Hubbard model (BHM) for fillings $n=1$, $n=2$, and $n=3$ by studying the single-particle gap, the fidelity susceptibility, and the amplitude of Bloch oscillations via density-matrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the fidelity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermions, the amplitude of Bloch oscillations after a tilt of the lattice vanishes at the critical points. This indicates that Bloch oscillations can serve as a tool to detect the transition point in ongoing experiments with ultracold gases.

arXiv:1212.2219•Physical Review A•Apr 8, 2013•83 citations
In a quantum many-body system, dimensionality plays a critical role in determining the type of quantum phase transition. To study the quantum system during dimensional crossover, we studied the Bose-Hubbard model on a cubic lattice with anisotropic hopping by using the high-order symbolic strong-coupling expansion method. The analytic series expanded boundaries between the Mott insulator and the superfluid phase up to eighth order are calculated. The critical exponents are extracted by the Pad'e resummation method, which clearly shows dimensional crossover behavior. Meanwhile, the critical points at commensurate filling can also be obtained, and they match well with the prediction of renormalization group theory. Finally, the scaling of the gap energy and the whole phase diagram are given, and they can be taken as the benchmark for experiment and numerical simulations in future study.
Based on the process-chain method, we work out in detail a high-order strong-coupling expansion (HSCE) algorithm for determining the quantum phase boundary between the Mott insulator and the superfluid phase of the Bose-Hubbard model in different dimensions. A comparison with quantum Monte-Carlo results reveals the high efficiency and accuracy of the HSCE. With a symbolized evaluation of the algorithm we obtain an analytic expression for the strong-coupling boundary for different fillings up to eighth order. A subsequent Pad\'e approximation then yields a scaling function, which rescales lobes with different fillings to one lobe. As a further crosscheck, we perform a hopping expansion of the phase boundaries obtained from the effective potential Landau theory (EPLT) and find that the respective expansion coefficients coincide with those of HSCE.
Combining the process-chain method with a symbolized evaluation, we work out in detail a high-order symbolic strong-coupling expansion (HSSCE) for determining the quantum phase boundaries between the Mott insulator and the superfluid phase of the Bose-Hubbard model for different fillings in hypercubic lattices of different dimensions. With a subsequent Pad\'e approximation we achieve for the quantum phase boundaries a high accuracy, which is comparable to high-precision quantum Monte-Carlo simulations, and show that all the Mott lobes can be rescaled to a single one. As a further cross-check, we find that the HSSCE results coincide with a hopping expansion of the quantum phase boundaries, which follow from the effective potential Landau theory.
We compute the ground-state phase diagram of the two-dimensional (2D) Bose-Hubbard model with anisotropic hopping using quantum Monte Carlo simulations, connecting the one-dimensional (1D) to the 2D system. We find that the tip of the lobe lies on a curve controlled by the 1D limit over the full anisotropy range, while the universality class is always the same as in the isotropic 2D system. This behavior can be derived analytically from the lowest renormalization-group equations and has a shape typical for the underlying Kosterlitz-Thouless transition in one dimension. We also compute the phase boundary of the Mott lobe at unit density for strong anisotropy and compare it to the 1D system. Our calculations shed light on recent cold gas experiments monitoring the dynamics of an expanding cloud.
To analyze the ground-state phase diagram of Bose-Bose mixtures loaded into ddd-dimensional hypercubic optical lattices, we perform a strong-coupling power-series expansion in the kinetic energy term (plus a scaling analysis) for the two-species Bose-Hubbard model with onsite boson-boson interactions. We consider both repulsive and attractive interspecies interaction, and obtain an analytical expression for the phase boundary between the incompressible Mott insulator and the compressible superfluid phase up to third order in the hoppings. In particular, we find a re-entrant quantum phase transition from paired superfluid (superfluidity of composite bosons, i.e., Bose-Bose pairs) to Mott insulator and again to a paired superfluid in all one, two, and three dimensions, when the interspecies interaction is sufficiently large and attractive. We hope that some of our results could be tested with ultracold atomic systems.
We investigate the zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with power-law hopping decaying with distance as 1/r^{α} using exact large scale quantum Monte Carlo simulations. For all 1<α≤3 the quantum phase transition from a superfluid and a Mott insulator at unit filling is found to be continuous and scale invariant, in marked contrast with the Berezinskii-Kosterlitz-Thouless (BKT) scenario that is recovered only for α>3. By performing finite-size scaling collapses of the superfluid stiffness and extracting dynamical and correlation-length exponents from the low-energy spectrum, we establish that these transitions define a distinct universality class throughout the long-range regime 1<α≤3. Analysis of the single-particle correlation functions and grand canonical phase diagram further reveals a sequence of ordering regimes within the superfluid phase: true long-range order for α≤2, anomalous quasi-long-range order for 2<α≤3, and conventional algebraic decay for α>3. Our exact numerical results provide a benchmark to compare theories of long-range quantum models and are relevant for experiments with cold neutral atom, molecules and ion chains.
We investigate the interaction-induced superfluid-to-Mott-insulator transition in the one-dimensional Bose-Hubbard model (BHM) for fillings n=1n=1n=1, n=2n=2n=2, and n=3n=3n=3 by studying the single-particle gap, the fidelity susceptibility, and the amplitude of Bloch oscillations via density-matrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the fidelity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermions, the amplitude of Bloch oscillations after a tilt of the lattice vanishes at the critical points. This indicates that Bloch oscillations can serve as a tool to detect the transition point in ongoing experiments with ultracold gases.