Gap scaling at Berezinskii-Kosterlitz-Thouless quantum critical points in one-dimensional Hubbard and Heisenberg models

Abstract

We discuss how to locate critical points in the Berezinskii-Kosterlitz-Thouless (BKT) universality class by means of gap-scaling analyses. While accurately determining such points using gap extrapolation procedures is usually challenging and inaccurate due to the exponentially small value of the gap in the vicinity of the critical point, we show that a generic gap-scaling analysis, including the effects of logarithmic corrections, provides very accurate estimates of BKT transition points in a variety of spin and fermionic models. As a first example, we show how the scaling procedure, combined with density-matrix-renormalization-group simulations, performs extremely well in a non-integrable spin-$3/2$ XXZ model, which is known to exhibit strong finite-size effects. We then analyze the extended Hubbard model, whose BKT transition has been debated, finding results that are consistent with previous studies based on the scaling of the Luttinger-liquid parameter. Finally, we investigate an anisotropic extended Hubbard model, for which we present the first estimates of the BKT transition line based on large-scale density-matrix-renormalization-group simulations. Our work demonstrates how gap-scaling analyses can help to locate accurately and efficiently BKT critical points, without relying on model-dependent scaling assumptions.

arXiv comment8 pages, 7 figures

References in corpus (34)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group
• Entanglement Entropy and Quantum Field Theory
• Bosonization and Strongly Correlated Systems
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Berezinskii-Kosterlitz-Thouless Crossover in a Trapped Atomic Gas
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
• Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators
• Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
• Tricritical Behavior in the Extended Hubbard Chains
• Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model
• Ground-state phase diagram of a half-filled one-dimensional extended Hubbard model
• Ground state phases of the Half-Filled One-Dimensional Extended Hubbard Model
• Phase diagram of the one-dimensional half-filled extended Hubbard model
• Molecular superfluid phase in systems of one-dimensional multicomponent fermionic cold atoms
• Detecting Quantum Critical Points using Bipartite Fluctuations
• Dimerization in a half-filled one-dimensional extended Hubbard model
• Critical behavior of the S=3/2 antiferromagnetic Heisenberg chain
• Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model
• Ground-state phase diagram of the one-dimensional half-filled extended Hubbard model
• Spin-1/2 fermions on spin-dependent optical lattices
• Functional Renormalization Group Analysis of the Half-filled One-dimensional Extended Hubbard Model
• Possible Exotic Phases in the One-Dimensional Extended Hubbard Model
• Phase diagram of the half-filled one-dimensional t-V-V' model
• The Half-Filled One-Dimensional Extended Hubbard Model: Phase diagram and Thermodynamics
• Estimating Quasi-long-range Order via Renyi Entropies
• How Hidden Orders Generate Gaps in 1D Fermionic Systems
• Quantum information analysis of the phase diagram of the half-filled extended Hubbard model
• Critical properties and Rényi entropies of the spin-3/2 XXZ chain
• Some experimental tests of Tomonaga-Luttinger liquids
• Phase separation and pairing regimes in the one-dimensional asymmetric Hubbard model
• A renormalization group analysis of the one-dimensional extended Hubbard model
• Pairing, crystallization and string correlations of mass-imbalanced atomic mixtures in one-dimensional optical lattices
• Resistance scaling at the Kosterlitz-Thouless transition

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