We propose a two-dimensional hard-core loop-gas model as a way to regularize the asymptotically free massive continuum quantum field theory that emerges at the Berezinskii-Kosterlitz-Thouless transition. Without fine-tuning, our model can reproduce the universal step-scaling function of the classical lattice XY model in the massive phase as we approach the phase transition. This is achieved by lowering the fugacity of Fock-vacuum sites in the loop-gas configuration space to zero in the thermodynamic limit. Some of the universal quantities at the Berezinskii-Kosterlitz-Thouless transition show smaller finite size effects in our model as compared to the traditional XY model. Our model is a prime example of qubit regularization of an asymptotically free massive quantum field theory in Euclidean space-time and helps understand how asymptotic freedom can arise as a relevant perturbation at a decoupled fixed point without fine-tuning.
We propose a two-dimensional hard-core loop-gas model as a way to regularize the asymptotically free massive continuum quantum field theory that emerges at the Berezinskii-Kosterlitz-Thouless transition. Without fine-tuning, our model can reproduce the universal step-scaling function of the classical lattice XY model in the massive phase as we approach the phase transition. This is achieved by lowering the fugacity of Fock-vacuum sites in the loop-gas configuration space to zero in the thermodynamic limit. Some of the universal quantities at the Berezinskii-Kosterlitz-Thouless transition show smaller finite size effects in our model as compared to the traditional XY model. Our model is a prime example of qubit regularization of an asymptotically free massive quantum field theory in Euclidean space-time and helps understand how asymptotic freedom can arise as a relevant perturbation at a decoupled fixed point without fine-tuning.
Other than the commonly used Wilson’s regularization of quantum field theories (QFTs), there is a growing interest in regularizations that explore lattice models with a strictly finite local Hilbert space, in anticipation of the upcoming era of quantum simulations of QFTs. A notable example is Euclidean qubit regularization, which provides a natural way to recover continuum QFTs that emerge via infrared fixed points of lattice theories. Can such regularizations also capture the physics of ultraviolet fixed points? We present a novel regularization of the asymptotically free massive continuum QFT that emerges at the Berezenski-Kosterlitz-Thouless (BKT) transition through a hard core loop-gas model, discussing the advantages this model provides compared to traditional regularizations. In particular, we demonstrate that without the need for fine-tuning, it can reproduce the universal step-scaling function of the classical lattice XY model in the massive phase as we approach the phase transition.
Other than the commonly used Wilson's regularization of quantum field theories (QFTs), there is a growing interest in regularizations that explore lattice models with a strictly finite local Hilbert space, in anticipation of the upcoming era of quantum simulations of QFTs. A notable example is Euclidean qubit regularization, which provides a natural way to recover continuum QFTs that emerge via infrared fixed points of lattice theories. Can such regularizations also capture the physics of ultraviolet fixed points? We present a novel regularization of the asymptotically free massive continuum QFT that emerges at the Berezenski-Kosterlitz-Thouless (BKT) transition through a hard core loop-gas model, discussing the advantages this model provides compared to traditional regularizations. In particular, we demonstrate that without the need for fine-tuning, it can reproduce the universal step-scaling function of the classical lattice XY model in the massive phase as we approach the phase transition.
We study the universal critical behavior of two-dimensional (2D) lattice bosonic gases at the Berezinskii-Kosterlitz-Thouless (BKT) transition, which separates the low-temperature superfluid phase from the high-temperature normal phase. For this purpose, we perform quantum Monte Carlo simulations of the hard-core Bose-Hubbard (BH) model at zero chemical potential. We determine the critical temperature by using a matching method that relates finite-size data for the BH model with corresponding data computed in the classical XY model. In this approach, the neglected scaling corrections decay as inverse powers of the lattice size L, and not as powers of 1/lnL, as in more standard approaches, making the estimate of the critical temperature much more reliable. Then, we consider the BH model in the presence of a trapping harmonic potential, and we verify the universality of the trap-size dependence at the BKT critical point. This issue is relevant for experiments with quasi-2D trapped cold atoms.
We consider the 2d XY Model with topological lattice actions, which are invariant against small deformations of the field configuration. These actions constrain the angle between neighbouring spins by an upper bound, or they explicitly suppress vortices (and anti-vortices). Although topological actions do not have a classical limit, they still lead to the universal behaviour of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition — at least up to moderate vortex suppression. In the massive phase, the analytically known Step Scaling Function (SSF) is reproduced in numerical simulations. However, deviations from the expected universal behaviour of the lattice artifacts are observed. In the massless phase, the BKT value of the critical exponent ηc is confirmed. Hence, even though for some topological actions vortices cost zero energy, they still drive the standard BKT transition. In addition we identify a vortex-free transition point, which deviates from the BKT behaviour.
The classical Heisenberg model is one of the most fundamental models in statistical and condensed matter physics. Extensive theoretical and numerical studies suggest that, in two dimensions, this model does not exhibit a finite-temperature phase transition but instead manifests asymptotic freedom. However, some research has also proposed the possibility of a Berezinskii-Kosterlitz-Thouless (BKT) phase transition over the years. In this study, we revisit the classical two-dimensional (2D) Heisenberg model through large-scale simulations with linear system sizes up to L=16384. Our Monte Carlo data, without any extrapolation, clearly reveal an exponential divergence of the correlation length $\ensuremath{\xi}$ as a function of the inverse temperature $\ensuremath{\beta}$, a hallmark of asymptotic freedom. Moreover, extrapolating $\ensuremath{\xi}$ to the thermodynamic limit in the low-temperature regime achieves close agreement with the three-loop perturbative calculations. We further propose a finite-size scaling (FSS) ansatz for $\ensuremath{\xi}$, demonstrating that the pseudocritical point ${\ensuremath{\beta}}_{L}$ diverges logarithmically with L. The thermodynamic and finite-size scaling behaviors of the magnetic susceptibility $\ensuremath{\chi}$ are also investigated and corroborate the predictions of asymptotic freedom. Our paper provides solid evidence for asymptotic freedom in the 2D Heisenberg model and advances understanding of finite-size scaling in such systems.
We investigate the 2d XY model by using the constraint angle action, which belongs to the class of topological lattice actions. These actions violate important features usually demanded for a lattice action, such as the correct classical continuum limit and the applicability of perturbation theory. Nevertheless, they still lead to the same universal quantum continuum limit and show excellent scaling behavior. By using the constraint angle action we gain new insight into the Berezinskii-Kosterlitz-Thouless phase transition of the 2d XY model. This phase transition is of special interest since it is one of the few examples of a phase transition beyond second order. It is of infinite order and therefore an essential phase transition. In particular, we observe an excellent scaling behavior of the helicity modulus, which characterizes this phase transition. We also observe that the mechanism of (un)binding vortex-anti-vortex pairs follows the usual pattern, although free vortices do not require any energy in the formulation of the 2d XY model using the constraint angle action.