$BKT$ transitions in classical and quantum long-range systems

Abstract

In the past decades considerable efforts have been made in order to understand the critical features of both classical and quantum long-range interacting models. The case of the Berezinskii-Kosterlitz-Thouless (BKT) universality class, as in the $2d$ classical $XY$ model, is considerably complicated by the presence, for short-range interactions, of a line of renormalization group fixed points. In this paper we discuss a field theoretical treatment of the $2d$ $XY$ model with long-range couplings and we compare it with results from the self-consistent harmonic approximation. These methods lead to a rich phase diagram, where both power-law BKT scaling and spontaneous symmetry breaking appear for the same (intermediate) decay rates of long-range interactions. We also discuss the Villain approximation for the $2d$ $XY$ model with power-law couplings, providing hints that, in the long-range regime, it fails to reproduce the correct critical behavior. The obtained results are then applied to the long-range quantum XXZ spin chain at zero temperature. We discuss the relation between the phase diagrams of the two models and we give predictions about the scaling of the order parameter of the quantum chain close to the transition.

15 pages, 3 figures

References in corpus (9)

• Probing many-body dynamics on a 51-atom quantum simulator
• Quantum computing with trapped ions
• Cold atoms in cavity-generated dynamical optical potentials
• Observation of the Berezinskii-Kosterlitz-Thouless Phase Transition in an Ultracold Fermi Gas
• Quantum critical behaviour in the superfluid density of strongly underdoped ultrathin cuprate films
• Anisotropic Long-Range Spin Systems
• Evidence of Two-Dimensional Quantum Critical Behavior in the Superfluid Density of Deeply Underdoped Bi2Sr2CaCu2O8+x
• Correlated Non-Gaussian phase fluctuations in LaAlO${}_3$/SrTiO${}_3$ heterointerface
• Self-consistent harmonic approximation with non-local couplings

Cited by in corpus (23)

• Continuous Symmetry Breaking in a Trapped-Ion Spin Chain
• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• Melting of the two-dimensional solid phase in the Gaussian-core model
• Two-dimensional XY Ferromagnet Induced by Long-range Interaction
• Villain model with long-range couplings
• Transverse-field $XY$ spin chain with the competing long-range interactions: Multi-criticality around the $XX$-symmetric point
• Localization induced by spatially uncorrelated subohmic baths in one dimension
• The Nonclassical Regime of the Two-dimensional Long-range XY Model: a Comprehensive Monte Carlo Study
• Antiferromagnetic order enhanced by local dissipation
• Mapping a dissipative quantum spin chain onto a generalized Coulomb gas
• Tunneling with physics-informed RG flows in the anharmonic oscillator
• Helicity modulus in the bilayer XY model by worm algorithm
• Vortex supersolid in the XY model with tunable vortex fugacity
• Simulating the Berezinskii-Kosterlitz-Thouless Transition with Complex Langevin
• Compensation in trilayered anisotropic 6-state clock model
• High-temperature partition functions and classical simulatability of long-range quantum systems
• Field-induced magnon decays in dipolar quantum magnets
• Long-Range Order in a Strictly Short-Range Quasi-2D XY Model: When Critical Fluctuations Matter
• Crossover in the Ordered Phase in the Non-Mermin-Wagner-Hohenberg Regime of Spin Models with Long-Range Coupling
• Anomalous criticality coexists with giant cluster in the uniform forest model
• Persistence of the Berezinskii-Kosterlitz-Thouless transition with long-range couplings
• One-dimensional long-range Ising model: two (almost) equivalent approximations
• Stability of current-carrying states in hard-core bosons with long-range hopping on a square lattice