Transition-type change between an inverted Berezinskii-Kosterlitz-Thouless transition and an abrupt transition in the bond percolation on a random hierarchical small-world network
We study bond percolation on a one-parameter family of hierarchical small-world network, and find a meta-transition between the inverted BKT transition and the abrupt transition driven by changing the network topology. It is found that the order parameter is continuous and fractal exponent is discontinuous in the inverted BKT transition, and oppositely, the former is discontinuous and the latter is continuous in the abrupt transition. The gaps of the order parameter and fractal exponent in each transition go to vanish as approaching the meta-transition point. This point corresponds to a marginal power-law transition. In the renormalization group formalism, this meta-transition corresponds to the transition between transcritical and saddle-node bifurcations of the fixed point via a pitchfork bifurcation.
We perform Monte Carlo simulations to study the two dimensional random-bond XY model on a square lattice. Two kinds of bond randomness with the coupling coefficient obeying the Gaussian or uniform distribution are discussed. It is shown that the two kinds of disorder lead to similar thermodynamic behaviors if their variances take the same value. This result implies that the variance can be chosen as a characteristic parameter to evaluate the strength of the randomness. In addition, the Berezinskii-Kosterlitz-Thouless transition temperature decreases as the variance increases and the transition…
We develop a gauge theory of the critical behavior of the topological excitations-driven Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the XY model with weak quenched disorder. We find that while in two-dimensions the liquid of topological defects exhibits the BKT critical behavior, the three-dimensional system shows more singular Vogel-Fulcher-Tamman criticality heralding its freezing into a spin glass. Our findings provide insights into the topological origin of spin glass formation.
Berezinskii-Kosterlitz-Thouless transition of the classical XY model is re-investigated, combining the Tensor Network Renormalization (TNR) and the Level Spectroscopy method based on the finite-size scaling of the Conformal Field Theory. By systematically analyzing the spectrum of the transfer matrix of the systems of various moderate sizes which can be accurately handled with a finite bond dimension, we determine the critical point removing the logarithmic corrections. This improves the accuracy by an order of magnitude over previous studies including those utilizing TNR. Our analysis also gi…
Phase diagram of S=1 XXZ chain in a staggered magnetic field is obtained numerically. The Berezinskii-Kosterlitz-Thouless transition between the XY and the antiferromagnetic phases is studied by the level-spectroscopy. Moreover we find that there is no distinction between the Haldane and the antiferromagnetic phases, since the Gaussian critical line does not appear, in contrast to the $S=1/2$ case. It is expected that some hidden $Z_2\times Z_2$ symmetry breaking happens not only in the Haldane phase but also in the antiferromagnetic one.
Using Monte Carlo simulations and finite-size scaling, we study three-state Potts antiferromagnet on layered square lattice with two and four layers $L_z=2$ and $4$. As temperature decreases, the system develops quasi-long-range order via a Berezinskii-Kosterlitz-Thouless transition at finite temperature $T_{c1}$. For $L_z=4$, as temperature is further lowered, a long-range order breaking the $Z_6$ symmetry develops at a second transition at $T_{c2} < T_{c1}$. The transition at $T_{c2}$ is also Berezinskii-Kosterlitz-Thouless-like, but has magnetic critical exponent $η=1/9$ instead of the conv…
The field-induced Berezinskii-Kosterlitz-Thouless (BKT) transition in the ground state of the triangular antiferromagnetic Ising model is studied by the level-spectroscopy method. We analyze dimensions of operators around the BKT line, and estimate the BKT point $H_{\rm c}\simeq0.5229\pm0.001$, which is followed by a level-consistency check to demonstrate the accuracy of our estimate. Further we investigate the anisotropic case to clarify the stability of the field-induced string-density plateau against an incommensurate liquid state by the density-matrix renormalization-group method.
We study the flux noise in Josephson junction arrays in the critical regime above the Berezinskii-Kosterlitz-Thouless transition. In proximity coupled arrays a local ohmic damping for the phases is relevant, giving rise to anomalous vortex diffusion and a dynamic scaling of the flux noise in the critical region. It shows a crossover from white to $1/f$-noise at a frequency $ω_ξ\proptoξ^{-z}$ with a dynamic exponent $z=2$.
We embody the density matrix renormalization group (DMRG) method for the 19-vertex model on a square lattice in order to investigate the Berezinskii-Kosterlitz-Thouless transition. Elements of the transfer matrix of the 19-vertex model are classified in terms of the total value of arrows in one layer of the square lattice. By using this classification, we succeed to reduce enormously the dimension of the matrix which has to be diagonalized in the DMRG method. We apply our method to the 19-vertex model with the interaction $K=1.0866$ and obtain $c=1.006(1)$ for the conformal anomaly. PACS. 05.9…
Classical 2D clock model is known to have a critical phase with Berezinskii-Kosterlitz-Thouless(BKT) transitions. These transitions have logarithmic corrections which make numerical analysis difficult. In order to resolve this difficulty, one of the authors has proposed the method called level spectroscopy, which is based on the conformal field theory. We extend this method to the multi-degenerated case. As an example, we study the classical 2D 6-clock model which can be mapped to the quantum self-dual 1D 6-clock model. Additionally, we confirm that the self-dual point has a precise numerical …
We study $q$-state clock models of regular and Villain types with $q=5,6$ using cluster-spin updates and observed double transitions in each model. We calculate the correlation ratio and size-dependent correlation length as quantities for characterizing the existence of Berezinskii-Kosterlitz-Thouless (BKT) phase and its transitions by large-scale Monte Carlo simulations. We discuss the advantage of correlation ratio in comparison to other commonly used quantities in probing BKT transition. Using finite size scaling of BKT type transition, we estimate transition temperatures and corresponding …
The Berezinskii-Kosterlitz-Thouless (BKT) phase transition is considered in the condition of lowest temperatures, when thermal fluctuations give place to quantum ones. For this goal, the critical dynamic of the Sine-Gordon model near the quantum critical point is considered. The approach based on the Keldysh-Schwinger technique of non-equilibrium dynamics description is used, as well as the method of taking into account the crossover from the thermal fluctuation regime to the quantum one in the renormalization group technique. For the system with low vortex concentration, it is shown that the …
Using the technique of supervised neural networks (NN), we study the phase transitions of two-dimensional (2D) 6- and 8-state clock models on the square lattice. The employed NN has only one input layer, one hidden layer of 2 neurons, and one output layer. In addition, the NN is trained without any prior information about the considered models. Interestingly, despite its simple architecture, the built supervised NN not only detects both the two Berezinskii--Kosterlitz--Thouless (BKT) transitions but also determines the transition temperatures with reasonable high accuracy. It is remarkable tha…
In statistical physics, the XY model in two dimensions provides the paradigmatic example of phase transitions mediated by topological defects (vortices). Over the years, a variety of analytical and numerical methods have been deployed in an attempt to fully understand the nature of its transition, which is of the Berezinskii-Kosterlitz-Thouless type. These met with only limited success until it was realized that subtle effects (logarithmic corrections) that modify leading behaviour must be taken into account. This realization prompted renewed activity in the field and significant progress has …
The two Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional 5-state clock model are studied on infinite strips using the DMRG algorithm. Because of the open boundary conditions, the helicity modulus $Υ_2$ is computed by imposing twisted magnetic fields at the two boundaries. Its scaling behavior is in good agreement with the existence of essential singularities with $σ=1/2$ at the two transitions. The predicted universal values of $Υ_2$ are shown to be reached in the thermodynamic limit. The fourth-order helicity modulus is observed to display a dip at the high-temperature…
We develop a new functional renormalization group (FRG) approach for the two-dimensional XY-model by combining the lattice FRG proposed by Machado and Dupuis [Phys. Rev. E 82, 041128 (2010)] with a duality transformation which explicitly introduces vortices via an integer-valued field. We show that the hierarchy of FRG flow equations for the infinite set of relevant and marginal couplings of the model can be reduced to the well-known Kosterlitz-Thouless renormalization group equations for the renormalized temperature and the vortex fugacity. Within our approach it is straightforward to include…
We investigate the possibility that Bose-Einstein condensates (BECs), loaded on a 2D optical lattice, undergo - at finite temperature - a Berezinskii-Kosterlitz-Thouless (BKT) transition. We show that - in an experimentally attainable range of parameters - a planar lattice of BECs is described by the XY model at finite temperature. We demonstrate that the interference pattern of the expanding condensates provides the experimental signature of the BKT transition by showing that, near the critical temperature, the k=0 component of the momentum distribution and the central peak of the atomic dens…
A comparison between the Kosterlitz-Thouless theory of metal insulator transition in a two dimensional plasma and a counterion condensation in a polyelectrolyte solution is made. It is demonstrated that, unlike some of the recent suggestions, the counterion condensation and the Kosterlitz-Thouless transition are distinct.
We show that supersymmetry emerges in a large class of models in 1+1 dimensions with both Z_2 and U(1) symmetry at the multicritical point where the Ising and Berezinskii-Kosterlitz-Thouless transitions coincide. To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations allowed by symmetry. This analysis reveals an intricate flow with a marginally irrelevant direction that preserves part of the supersymmetry of the fixed point. The slow flow along this special line has significant consequences on the physics of the mul…
We analyse the Bose-Einstein condensation process and the Berezinskii-Kosterlitz-Thouless phase transition within the Gross-Pitaevskii model and their interplay with wave turbulence theory. By using numerical experiments we study how the condensate fraction and the first order correlation function behave with respect to the mass, the energy and the size of the system. By relating the free-particle energy to the temperature we are able to estimate the Berezinskii-Kousterlitz-Thouless transition temperature. Below this transition we observe that for a fixed temperature the superfluid fraction ap…
A numerical study of the neutral two-dimensional (2D) lattice Coulomb gas is performed to examine dynamic scaling, finite size effects, and the dynamic critical exponent $z$ of the Kosterlitz-Thouless-Berezinskii transition. By studying large system sizes ($L=100$), we show $z=2.0 \pm0.2$ using Fisher-Fisher-Huse (FFH) scaling. We also present evidence that the vortex correlation length is finite below the transition temperature, in contrast to conventional wisdom. Finally, we conclude that previous findings for a variety of experimental systems that $z\simeq 5.6$ using FFH scaling indicates t…
Using the two dimensional $XY-(S(O(3))$ model as a test case, we show that analysis of the Fisher zeros of the canonical partition function can provide signatures of a transition in the Berezinskii-Kosterlitz-Thouless ($BKT$) universality class. Studying the internal border of zeros in the complex temperature plane, we found a scenario in complete agreement with theoretical expectations which allow one to uniquely classify a phase transition as in the $BKT$ class of universality. We obtain $T_{BKT}$ in excellent accordance with previous results. A careful analysis of the behavior of the zeros …
The Berezinskii-Kosterlitz-Thouless transition is a very specific phase transition where all thermodynamic quantities are smooth. Therefore, it is difficult to determine the critical temperature in a precise way. In this paper we demonstrate how neural networks can be used to perform this task. In particular, we study how the accuracy of the transition identification depends on the way the neural networks are trained. We apply our approach to three different systems: (i) the classical XY model, (ii) the phase-fermion model, where classical and quantum degrees of freedom are coupled and (iii) t…
Evidence for a Kosterlitz-Thouless transition in the 2D step model is obtained from Monte Carlo determinations of the helicity modulus. It is argued that the free energy of a single vortex at the center of the system depends logarithmically on the system size in spite of the fact that the spin interaction is not harmonic for small differences in the spin angles. We conclude that this is the reason for the Kosterlitz-Thouless transition in the 2D step model and that the harmonic spin interaction not is a necessary requirement.
Ordering of the geometrically frustrated two-dimensional Heisenberg antiferromagnet on a pyrochlore slab is studied by Monte Carlo simulations. In contrast to the kagomé Heisenberg antiferromagnet, the model exhibits locally non-coplanar spin structures at low temperatures, bearing nontrivial chiral degrees of freedom. Under certain conditions, the model exhibits a novel Kosterlitz-Thouless-type transition at a finite temperature associated with these chiral degrees of freedom.
We demonstrate that a machine learning technique with a simple feedforward neural network can sensitively detect two successive phase transitions associated with the Berezinskii-Kosterlitz-Thouless (BKT) phase in q-state clock models simultaneously by analyzing the weight matrix components connecting the hidden and output layers. We find that the method requires only a data set of the raw spatial spin configurations for the learning procedure. This data set is generated by Monte-Carlo thermalizations at selected temperatures. Neither prior knowledge of, for example, the transition temperatures…
Berezinskii-Kosterlitz-Thouless phase transitions of the antiferromagnetic Ising model with ferromagnetic next-nearest-neighbor interactions on the kagome lattice
We evaluate the charge and spin susceptibilities of the 2D attractive Hubbard model and we compare our results with Montecarlo simulations on the same model. We discuss the possibility to include topological Kosterlitz-Thouless superconducting fluctuations in a standard perturbative approach substituting in the fluctuation propagator the Ginzburg-Landau correlation length with the Kosterlitz-Thouless correlation length.
We investigate the general features of the renormalization-group flow at the Berezinskii-Kosterlitz-Thouless (BKT) transition, providing a thorough quantitative description of the asymptotc critical behavior, including the multiplicative and subleading logarithmic corrections. For this purpose, we consider the RG flow of the sine-Gordon model around the renormalizable point which describes the BKT transition. We reduce the corresponding beta-functions to a universal canonical form, valid to all perturbative orders. Then, we determine the asymptotic solutions of the RG equations in various crit…
Two dimensional systems with U(1) symmetry exhibit a peculiar phase, i.e., the Berezinskii-Kosterlitz-Thouless (BKT) phase. In particular situations, the BKT phase exists as an intermediate temperature phase. There have been scenarios for the phase transitions at the two endpoints of the intermediate BKT phase, i.e., the phase transition at the low-temperature endpoint is a BKT transition and that at the high-temperature endpoint is either a BKT transition or a first-order transition. The present study gives a novel scenario, i.e., a second-order transition with a new critical universality and…
We study the critical point for the emergence of coherence in a harmonically trapped two-dimensional Bose gas with tuneable interactions. Over a wide range of interaction strengths we find excellent agreement with the classical-field predictions for the critical point of the Berezinskii-Kosterlitz-Thouless (BKT) superfluid transition. This allows us to quantitatively show, without any free parameters, that the interaction-driven BKT transition smoothly converges onto the purely quantum-statistical Bose-Einstein condensation (BEC) transition in the limit of vanishing interactions.
The two-dimensional $S=1/2$ XY model is investigated with an extensive quantum Monte Carlo simulation. The helicity modulus is precisely estimated through a continuous-time loop algorithm for systems up to $128 \times 128$ near and below the critical temperature. The critical temperature is estimated as $T_{\rm KT} = 0.3427(2)J$. The obtained estimates for the helicity modulus are well fitted by a scaling form derived from the Kosterlitz renormalization group equation. The validity of the Kosterlitz-Thouless theory for this model is confirmed.
A new approach to the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional Coulomb gas model is explored by MC simulation and finite size scaling. The usual mapping of a neutral two-dimensional superconductor in zero magnetic field to a Coulomb gas leads to an unscreened logarithmic interaction between the vortices, and with periodic boundary conditions vortex configurations are always vorticity neutral with an equal number of plus and minus vortices. We demonstrate that relaxing the neutrality condition has certain advantages. It leads to non-neutral vortex configurations that ca…
We study the Berezinskii-Kosterlitz-Thouless (BKT) transition of two-component Bose mixtures in two spatial dimensions. When phases of both components are decoupled, half-quantized vortex-antivortex pairs of each component induce two-step BKT transitions. On the other hand, when phases of the both components are synchronized through the inter-component Josephson coupling, two species of vortices of each component are bind to form a molecule, and in this case, we find that there is only one BKT transition by molecule-antimolecule pairs. Our results can be tested by two weakly-connected Bose sys…
The 2016 Physics Nobel Prize honors a variety of discoveries related to topological phases and phase transitions. Here we sketch two exciting facets: the groundbreaking works by John Kosterlitz and David Thouless on phase transitions of infinite order, and by Duncan Haldane on the energy gaps in quantum spin chains. These insights came as surprises in the 1970s and 1980s, respectively, and they have both initiated new fields of research in theoretical and experimental physics.
The Berezinskii-Kosterlitz-Thouless (BKT) mechanism describes the breakdown of superfluidity in a two-dimensional Bose gas or a two-dimensional gas of paired fermions. In the latter case, a population imbalance between the two pairing partners in the Fermi mixture is known to influence pairing characteristics. Here, we investigate the effects of imbalance on the two-dimensional BKT superfluid transition, and show that superfluidity is even more sensitive to imbalance than for three dimensional systems. Finite-temperature phase diagrams are derived using the functional integral formalism in com…
For the inverse square long-range ferromagnetic Ising chain in a transverse field, the thermal phase boundary of the floating Kosterlitz-Thouless phase is obtained for several values of the transverse field down to the quantum critical point. The sharp domain walls in the classical model are increasingly smeared out by the transverse field, which is evidenced by a pronounced broadening of the non-universal bump in the specific heat. The discernability of KT critical scaling in finite-size simulations is discussed.
The Berezinskii-Kosterlitz-Thouless (BKT) phase transition drives the unbinding of topological defects in many two-dimensional systems. In the two-dimensional Coulomb gas, it corresponds to an insulator-conductor transition driven by charge deconfinement. We investigate the global topological properties of this transition, both analytically and by numerical simulation, using a lattice-field description of the two-dimensional Coulomb gas on a torus. The BKT transition is shown to be an ergodicity breaking between the topological sectors of the electric field, which implies a definition of topol…
We study the phase diagram and critical behavior of a two-dimensional lattice SO($N_c$) gauge theory ($N_c \ge 3$) with two scalar flavors, obtained by partially gauging a maximally O($2N_c$) symmetric scalar model. The model is invariant under local SO($N_c$) and global O(2) transformations. We show that, for any $N_c \ge 3$, it undergoes finite-temperature Berezinskii-Kosterlitz-Thouless (BKT) transitions, associated with the global Abelian O(2) symmetry. The transition separates a high-temperature disordered phase from a low-temperature spin-wave phase where correlations decay algebraically…
We have considered two classical lattice-gas models, consisting of particles that carry multicomponent magnetic momenta, and associated with a two-dimensional square lattices; each site can host one particle at most, thus implicitly allowing for hard-core repulsion; the pair interaction, restricted to nearest neighbors, is ferromagnetic and involves only two components. The case of zero chemical potential has been investigated by Grand--Canonical Monte Carlo simulations; the fluctuating occupation numbers now give rise to additional fluid-like observables in comparison with the usual saturated…
We investigate the Berezinskii-Kosterlitz-Thouless transitions for the square-lattice six-state clock model with the corner-transfer matrix renormalization group (CTMRG). Scaling analyses for effective correlation length, magnetization, and entanglement entropy with respect to the cutoff dimension $m$ at the fixed point of CTMRG provide transition temperatures consistent with a variety of recent numerical studies. We also reveal that the fixed point spectrum of the corner transfer matrix in the critical intermediate phase of the six-state clock model is characterized by the scaling dimension c…
With a rigorous renormalization group approach, we study the pressure of the two dimensional Coulomb Gas along a small piece of the Kosterlitz-Thouless transition line, i.e. the boundary of the dipole region in the activity-temperature phase-space.
We study the one-dimensional Bose-Hubbard model describing the superfluid-Mott insulator quantum phase transition of cold atoms in optical lattices. We show that derivatives of the variance of the on-site atom number occupation, computed with respect to the parameter driving the transition, have extrema that are located off the critical point even in the thermodynamic limit. We discuss whether such extrema provide solid evidence of the quantum Berezinskii-Kosterlitz-Thouless transition taking place in this system. The calculations are done for systems with the mean number of atoms per lattice …
We study the quasi-two-dimensional quantum O(2) model, a quantum generalization of the Lawrence-Doniach model, within the nonperturbative renormalization-group approach and propose a generic phase diagram for layered three-dimensional systems with an O(2)-symmetric order parameter. Below the transition temperature we identify a wide region of the phase diagram where the renormalization-group flow is quasi-two-dimensional for length scales smaller than a Josephson length $l_J$, leading to signatures of Kosterlitz-Thouless physics in the temperature dependence of physical observables. In particu…
The "canonical" variables of the Kosterlitz-Thouless theory--fields $Φ_0({\bf r})$ and $ϕ({\bf r})$, generally believed to stand for vortices and phonons (or their XY equivalents, like spin waves, etc.) turn out to be neither vortices and phonons, nor, strictly speaking, {\it canonical} variables. The latter fact explains paradoxes of (i) absence of interaction between $Φ_0$ and $ϕ$, and (ii) non-physical contribution of small vortex pairs to long-range phase correlations. We resolve the paradoxes by explicitly relating $Φ_0$ and $ϕ$ to canonical vortex-pair and phonon variables.
We extend a Gaussian model for the internal electrical potential of a two-dimensional Coulomb gas by a non-Gaussian measure term, which singles out the physically relevant configurations of the potential. The resulting Hamiltonian, expressed as a functional of the internal potential, has a surprising large-scale limit: The additional term simply counts the number of maxima and minima of the potential. The model allows for a transparent derivation of the divergence of the correlation length upon lowering the temperature down to the Kosterlitz-Thouless transition point.
Despite tremendous theoretical efforts to understand subtleties of the many-body localization (MBL) transition, many questions remain open, in particular concerning its critical properties. Here we make the key observation that MBL in one dimension is accompanied by a spin freezing mechanism which causes chain breakings in the thermodynamic limit. Using analytical and numerical approaches, we show that such chain breakings directly probe the typical localization length, and that their scaling properties at the MBL transition agree with the Kosterlitz-Thouless scenario predicted by phenomenolog…
We introduce and study the properties of a periodic model interpolating between the sine-- and the sinh--Gordon theories in $1+1$ dimensions. This model shows the peculiarities, due to the preservation of the functional form of their potential across RG flows, of the two limiting cases: the sine-Gordon, not having conventional order/magnetization at finite temperature, but exhibiting Berezinskii-Kosterlitz-Thouless (BKT) transition; and the sinh-Gordon, not having a phase transition, but being integrable. The considered interpolation, which we term as {\em sn-Gordon} model, is performed with p…
We study the behaviour of the Binder cumulant on finite square lattices at the Kosterlitz-Thouless phase transition. We determine the fixed point value of the Binder cumulant and the coefficient of the leading logarithmic correction. These calculations are supplemented with Monte Carlo simulations of the classical XY (plane rotator) model, the Villain model and the dual of the absolute value solid-on-solid model. Using the single cluster algorithm, we simulate lattices up to L=4096. For the lattice sizes reached, subleading corrections are needed to fit the data for the Binder cumulant. We dem…
We investigate the nature of the phase transition occurring in a planar XY-model spin system with dipole-dipole interactions. It is demonstrated that a Berezinskii-Kosterlitz-Thouless (BKT) type of phase transition always takes place at a finite temperature separating the ordered (ferro) and the disordered (para) phases. The low-temperature phase corresponds to an ordered state with thermal fluctuations, composed of a "gas" of bound vortex-antivortex pairs, which would, when considered isolated, be characterized by a constant vortex-antivortex attraction force which is due to the dipolar inter…
In this Letter we will show that, in the presence of a properly modulated Dzyaloshinskii-Moriya (DM) interaction, a $U(1)$ vortex-antivortex lattice appears at low temperatures for a wide range of the DM interaction. Even more, in the region dominated by the exchange interaction, a standard BKT transition occurs. In the opposite regime, the one dominated by the DM interaction, a kind of inverse BKT transition (iBKT) takes place. As temperature rises, the vortex-antivortex lattice starts melting by annihilation of pairs of vortex-antivortex, in a sort of "inverse" BKT transition.
We numerically study the Berezinskii-Kosterlitz-Thouless (BKT) transition of a spin-1 spinor Bose gas under the quadratic Zeeman effect. A calculation of the mass and spin superfluid densities shows that (i) the BKT transition occurs only when vortices are classified by the integer group $\mathbb{Z}$, and $\mathbb{Z}_2$ vortices do not contribute to the BKT transition, (ii) the two BKT transition temperatures for mass and spin superfluid densities are different for a positive quadratic Zeeman effect and equal for a negative quadratic Zeeman effect, and (iii) the universal relation of the super…
The Kosterlitz-Thouless transition for the spin 1/2 Heisenberg chain with the next-to-the-nearest-neighbor interaction is investigated in the context of an infinite matrix product state algorithm, which is a generalization of the infinite time-evolving block decimation algorithm [G. Vidal, Phys. Rev. Lett. \textbf{98}, 070201 (2007)] to accommodate both the next-to-the-nearest-neighbor interaction and spontaneous dimerization. It is found that, in the critical regime, the algorithm automatically leads to infinite degenerate ground-state wave functions, due to the finiteness of the truncation d…
The spatial dependence of the superfluid density is calculated for the Kosterlitz-Thouless transition in the presence of hard-wall boundaries, for the case of a single wall bounding the half-infinite plane, and for a superfluid strip bounded by two walls. The boundaries induce additional vortices that cause the superfluid density to become anisotropic, with the tensor component perpendicular to the wall falling to zero at the wall, whereas the component parallel to the wall remains finite. The effects of the boundaries are found to extend over all measured length scales, since the correlation …
