Scaling Theories of Kosterlitz-Thouless Phase Transitions

Abstract

We propose scaling theories for Kosterlitz-Thouless (KT) phase transitions on the basis of the hallmark exponential growth of their correlation length. Finite-size scaling, finite-entanglement scaling, short-time critical dynamics, and finite-time scaling, as well as some of their combinations are studied. Relaxation times of both a usual power-law and an unusual power-law with a logarithmic factor are considered. Finite-size and finite-entanglement scaling forms somehow similar to a frequently employed ansatz are presented. The Kibble-Zurek scaling of topological defect density for a linear driving across the KT transition point is investigated in detail. An implicit equation for a rate exponent in the theory is derived and the exponent varies with the distance from the critical point and the driving rate consistent with relevant experiments. To verify the theories, we utilize the KT phase transition of a one-dimensional Bose-Hubbard model. The infinite time-evolving-block-decimation algorithm is employed to solve numerically the model for finite bond dimensions. Both a correlation length and an entanglement entropy in imaginary time and only the entanglement entropy in real-time driving are computed. Both the short-time critical dynamics in imaginary time and the finite-time scaling in real-time driving, both including the finite bond dimension, for the measured quantities are found to describe the numerical results quite well via surface collapses. The critical point is also estimated and confirmed to be $0.302(1)$ at the infinite bond dimension on the basis of the scaling form.

arXiv comment16 pages, 9 figures. A mistake in a finite-size scaling form corrected

References in corpus (74)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement Entropy and Quantum Field Theory
• Nonequilibrium dynamics of closed interacting quantum systems
• Entanglement in quantum critical phenomena
• Theory of Phase Ordering Kinetics
• Efficient classical simulation of slightly entangled quantum computations
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Efficient simulation of one-dimensional quantum many-body systems
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Transition from a strongly interacting 1D superfluid to a Mott insulator
• Berezinskii-Kosterlitz-Thouless Crossover in a Trapped Atomic Gas
• Cosmological Experiments in Condensed Matter Systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Detection of Symmetry Protected Topological Phases in 1D
• Universality of Phase Transition Dynamics: Topological Defects from Symmetry Breaking
• Scaling of entanglement support for Matrix Product States
• Observation of scale invariance and universality in two-dimensional Bose gases
• Generalized Dynamic Scaling for Critical Magnetic Systems
• Matrix-product-groundstates for one-dimensional spin-1 quantum antiferromagnets
• Observation of a 2D Bose-gas: from thermal to quasi-condensate to superfluid
• Emergence of coherence and the dynamics of quantum phase transitions
• Dynamic Monte Carlo Measurement of Critical Exponents
• Universal Window for Two Dimensional Critical Exponents
• The two dimensional XY model at the transition temperature: A high precision Monte Carlo study
• Time evolution algorithms for Matrix Product States and DMRG
• Critical Point of an Interacting Two-Dimensional Atomic Bose Gas
• The trapped two-dimensional Bose gas: from Bose-Einstein condensation to Berezinskii-Kosterlitz-Thouless physics
• Kibble-Zurek mechanism in colloidal monolayers
• Ultracold bosons with short-range interaction in regular optical lattices
• Breakdown of Scaling in the Nonequilibrium Critical Dynamics of the Two-Dimensional XY Model
• Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model
• The Energy-Scaling Approach to Phase-Ordering Growth Laws
• Quench dynamics of the 2d XY model
• Finite-size scaling method for the Berezinskii-Kosterlitz-Thouless transition
• Large-scale Monte Carlo simulation of two-dimensional classical XY model using multiple GPUs
• Phase diagram of the half-filled one-dimensional t-V-V' model
• Kibble-Zurek Mechanism and Finite-Time Scaling
• Phase-transitions induced by easy-plane anisotropy in the classical Heisenberg antiferromagnet on a triangular lattice: a Monte Carlo simulation
• Logarithmic Corrections in the 2D XY Model
• A strong-coupling analysis of two-dimensional O(N) sigma models with N<=2 on square, triangular and honeycomb lattices
• The Kosterlitz-Thouless Universality Class
• Logarithmic Corrections to Scaling in the Two Dimensional $XY$--Model
• Dynamics of a quantum phase transition in the 1D Bose-Hubbard model: excitations and correlations induced by a quench
• Generalized Dynamic Scaling for Critical Relaxations
• A quantitative study of the Kosterlitz-Thouless phase transition in a system of two-dimensional plane rotators ( XY model ) by high temperature expansions through ${\beta }^{20}$
• Slow quench dynamics of Mott-insulating regions in a trapped Bose gas
• Dynamic Simulations of the Kosterlitz-Thouless Phase Transition
• Gap scaling at Berezinskii-Kosterlitz-Thouless quantum critical points in one-dimensional Hubbard and Heisenberg models
• Theory of Driven Nonequilibrium Critical Phenomena
• High temperature study of the Kosterlitz-Thouless phase transition in the XY model on the triangular lattice
• Re-entrance and entanglement in the one-dimensional Bose-Hubbard model
• Does the XY Model have an integrable continuum limit?
• Critical points of the anyon-Hubbard model
• Universal short-time quantum critical dynamics in imaginary time
• Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitions
• Some experimental tests of Tomonaga-Luttinger liquids
• High-temperature expansion of the magnetic susceptibility and higher moments of the correlation function for the two-dimensional XY model
• Anomalous energetics and dynamics of moving vortices
• Critical Behaviour of the Two Dimensional Step Model
• Corrections to Scaling for the Two-dimensional Dynamic XY Model
• Generalized dynamic scaling for quantum critical relaxation in imaginary time
• Kosterlitz Thouless Universality in Dimer Models
• Exact Solution for Vortex Dynamics in Temperature Quenches of Two-Dimensional Superfluids
• Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures
• The square-lattice F model revisited: a loop-cluster update scaling study
• Scaling theory of entanglement entropy in confinements near quantum critical points
• Resistance scaling at the Kosterlitz-Thouless transition
• The Atick-Witten free energy, closed tachyon condensation and deformed Poincare' symmetry
• Self-similarity breaking: Anomalous nonequilibrium finite-size scaling and finite-time scaling
• Numerical simulations of a two-dimensional lattice grain boundary model
• Finite-size scaling at infinite-order phase transitions
• Scaling of the magnetic permeability at the Berezinskii-Kosterlitz-Thouless transition from Coulomb gas simulations

Cited by in corpus (12)

• Anomalous fractal scaling in two-dimensional electric networks
• Phase fluctuations in two-dimensional superconductors and pseudogap phenomenon
• Dynamical phase transition and scaling in the chiral clock Potts chain
• Dual dynamic scaling in deconfined quantum criticality
• Kibble-Zurek scaling of the superfluid-supersolid transition in an elongated dipolar gas
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Theory of Critical Phenomena with Long-Range Temporal Interaction
• Theory of Critical Phenomena with Memory
• Quantum phases of the biased two-chain-coupled Bose-Hubbard Ladder
• Relaxation Critical Dynamics in Measurement-induced Phase Transitions
• Berezinskii-Kosterlitz-Thouless Renormalization Group Flow at a Quantum Phase Transition
• Short-time critical dynamics in the classical cubic dimer model