Bilayer Coulomb phase of two-dimensional dimer models: Absence of power-law columnar order

Asymptotic Freedom at the Berezinskii-Kosterlitz-Thouless Transition without Fine-Tuning Using a Qubit Regularization

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.

Spontaneous layering and power-law order in the three-dimensional fully packed hard-plate lattice gas

We obtain the phase diagram of fully packed hard plates on the cubic lattice. Each plate covers an elementary plaquette of the cubic lattice and occupies its four vertices, with each vertex of the cubic lattice occupied by exactly one such plate. We consider the general case with fugacities s_{μ} for "μ plates," whose normal is the μ direction (μ=x,y,z). At and close to the isotropic point, we find, consistent with previous work, a phase with long-range sublattice order. When two of the fugacities s_{μ_{1}} and s_{μ_{2}} are comparable, and the third fugacity s_{μ_{3}} is much smaller, we find a spontaneously layered phase. In this phase, the system breaks up into disjoint slabs of width two stacked along the μ_{3} axis. μ_{1} and μ_{2} plates are preferentially contained entirely within these slabs, while plates straddling two successive slabs have a lower density. This corresponds to a twofold breaking of translation symmetry along the μ_{3} axis. In the opposite limit, with μ_{3}≫μ_{1}∼μ_{2}, we find a phase with long-range columnar order, corresponding to simultaneous twofold symmetry breaking of lattice translation symmetry in directions μ_{1} and μ_{2}. The spontaneously layered phases display critical behavior, with power-law decay of correlations in the μ_{1} and μ_{2} directions when the slabs are stacked in the μ_{3} direction, and represent examples of "floating phases" discussed earlier in the context of coupled Luttinger liquids and quasi-two-dimensional classical systems. We ascribe this remarkable behavior to the constrained motion of defects in this phase, and we sketch a coarse-grained effective field theoretical understanding of the stability of power-law order in this unusual three-dimensional floating phase.

Phases of the hard-plate lattice gas on a three-dimensional cubic lattice

We study the phase diagram of a lattice gas of 2×2×1 hard plates on the three-dimensional cubic lattice. Each plate covers an elementary plaquette of the cubic lattice, with the constraint that a site can belong to utmost one plate. We focus on the isotropic system, with equal fugacities for the three orientations of plates. We show, using grand canonical Monte Carlo simulations, that the system undergoes two phase transitions when the density of plates is increased: the first from a disordered fluid phase to a layered phase, and the second from the layered phase to a sublattice-ordered phase. In the layered phase, the system breaks up into disjoint slabs of thickness two along one spontaneously chosen Cartesian direction, corresponding to a twofold (Z_{2}) symmetry breaking of translation symmetry along the layering direction. Plates with normals perpendicular to this layering direction are preferentially contained entirely within these slabs, while plates straddling two adjacent slabs have a lower density, thus breaking the symmetry between the three types of plates. We show that the slabs exhibit two-dimensional power-law columnar order even in the presence of a nonzero density of vacancies. In contrast, interslab correlations of the two-dimensional columnar order parameter decay exponentially with the separation between the slabs. In the sublattice-ordered phase, there is twofold symmetry breaking of lattice translation symmetry along all three Cartesian directions. We present numerical evidence that the disordered to layered transition is continuous and consistent with universality class of the three-dimensional O(3) model with cubic anisotropy, while the layered to sublattice transition is first-order in nature.

Derivation of field theory for the classical dimer model using bosonization

We derive a field theory for the two-dimensional classical dimer model by applying bosonization to Lieb's (fermionic) transfer-matrix solution. Our constructive approach gives results that are consistent with the well-known height theory, previously justified based on symmetry considerations, but also fixes coefficients appearing in the effective theory and the relationship between microscopic observables and operators in the field theory. In addition, we show how interactions can be included in the field theory perturbatively, treating the case of the double dimer model with interactions within and between the two replicas. Using a renormalization-group analysis, we determine the shape of the phase boundary near the noninteracting point, in agreement with results of Monte Carlo simulations.

Fractional Brownian motion of worms in worm algorithms for frustrated Ising magnets

We study the distribution of lengths and other statistical properties of worms constructed by Monte Carlo worm algorithms in the power-law three-sublattice ordered phase of frustrated triangular and kagome lattice Ising antiferromagnets. Viewing each step of the worm construction as a position increment (step) of a random walker, we demonstrate that the persistence exponent θ and the dynamical exponent z of this random walk depend only on the universal power-law exponents of the underlying critical phase and not on the details of the worm algorithm or the microscopic Hamiltonian. Further, we argue that the detailed balance condition obeyed by such worm algorithms and the power-law correlations of the underlying equilibrium system together give rise to two related properties of this random walk: First, the steps of the walk are expected to be power-law correlated in time. Second, the position distribution of the walker relative to its starting point is given by the equilibrium position distribution of a particle in an attractive logarithmic central potential of strength η_{m}, where η_{m} is the universal power-law exponent of the equilibrium defect-antidefect correlation function of the underlying spin system. We derive a scaling relation, z=(2-η_{m})/(1-θ), that allows us to express the dynamical exponent z(η_{m}) of this process in terms of its persistence exponent θ(η_{m}). Our measurements of z(η_{m}) and θ(η_{m}) are consistent with this relation over a range of values of the universal equilibrium exponent η_{m} and yield subdiffusive (z>2) values of z in the entire range. Thus, we demonstrate that the worms represent a discrete-time realization of a fractional Brownian motion characterized by these properties.