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Register a new userKertesz Line in the Three-Dimensional Compact U(1) Lattice Higgs Model
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The three-dimensional lattice Higgs model with compact U(1) gauge symmetry and unit charge is investigated by means of Monte Carlo simulations. The full model with fluctuating Higgs amplitude is simulated, and both energy as well as topological observables are measured. The data show a Higgs and a confined phase separated by a well-defined phase boundary, which is argued to be caused by proliferating vortices. For fixed gauge coupling, the phase boundary consists of a line of first-order phase transitions at small Higgs self-coupling, ending at a critical point. The phase boundary then continues as a Kertesz line across which thermodynamic quantities are nonsingular. Symmetry arguments are given to support these findings.
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We consider three-dimensional higher-charge multicomponent lattice Abelian-Higgs (AH) models, in which a compact U(1) gauge field is coupled to an N-component complex scalar field with integer charge q, so that they have local U(1) and global SU(N) symmetries. We discuss the dependence of the phase diagram, and the nature of the phase transitions, on the charge q of the scalar field and the number N>1 of components. We argue that the phase diagram of higher-charge models presents three different phases, related to the condensation of gauge-invariant bilinear scalar fields breaking the global SU(N) symmetry, and to the confinement/deconfinement of external charge-one particles. The transition lines separating the different phases show different features, which also depend on the number N of components. Therefore, the phase diagram of higher-charge models substantially differs from that of unit-charge models, which undergo only transitions driven by the breaking of the global SU(N) symmetry, while the gauge correlations do not play any relevant role. We support the conjectured scenario with numerical results, based on finite-size scaling analyses of Monte Carlo simuations for doubly-charged unit-length scalar fields with small and large number of components, i.e. N=2 and N=25.
Puzzled by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in cite{Wenzel08}, we study a similar anisotropic spin-1/2 Heisenberg model on the honeycomb lattice. The critical point where the phase transition occurs due to the dimerization as well as the critical exponent $ u$ are analyzed in great detail. Remarkly, using most of the available data points in conjunction with the expected finite-size scaling ansatz with a sub-leading correction indeed leads to a consistent $ u = 0.691(2)$ with that calculated in cite{Wenzel08}. However by using the data with large number of spins $N$, we obtain $ u = 0.707(6)$ which agrees with the most accurate Monte Carlo O(3) value $ u = 0.7112(5)$ as well.
We investigate the phase diagram and critical behavior of three-dimensional multicomponent Abelian-Higgs models, in which an N-component complex field z_x^a of unit length and charge is coupled to compact quantum electrodynamics in the usual Wilson lattice formulation. We determine the phase diagram and study the nature of the transition line for N=2 and N=4. Two phases are identified, specified by the behavior of the gauge-invariant local composite operator Q_x^{ab} = bar{z}_x^a z_x^b - delta^{ab}/N, which plays the role of order parameter. In one phase, we have langle Q_x^{ab}rangle =0, while in the other Q_x^{ab} condenses. Gauge correlations are never critical: gauge excitations are massive for any finite coupling. The two phases are separated by a transition line. Our numerical data are consistent with the simple scenario in which the nature of the transition is independent of the gauge coupling. Therefore, for any finite positive value of the gauge coupling, we predict a continuous transition in the Heisenberg universality class for N=2 and a first-order transition for N=4. However, notable crossover phenomena emerge for large gauge couplings, when gauge fluctuations are suppressed. Such crossover phenomena are related to the unstable O(2N) fixed point, describing the behavior of the model in the infinite gauge-coupling limit.
We study interacting Majorana fermions in two dimensions as a low-energy effective model of a vortex lattice in two-dimensional time-reversal-invariant topological superconductors. For that purpose, we implement ab-initio quantum Monte Carlo simulation to the Majorana fermion system in which the path-integral measure is given by a semi-positive Pfaffian. We discuss spontaneous breaking of time-reversal symmetry at finite temperature.
We study numerically the spin-1/2 XXZ model in a field on an infinite Kagome lattice. We use different algorithms based on infinite Projected Entangled Pair States (iPEPS) for this, namely: (i) with simplex tensors and 9-site unit cell, and (ii) coarse-graining three spins in the Kagome lattice and mapping it to a square-lattice model with nearest-neighbor interactions, with usual PEPS tensors, 6- and 12-site unit cells. Similarly to our previous calculation at the SU(2)-symmetric point (Heisenberg Hamiltonian), for any anisotropy from the Ising limit to the XY limit, we also observe the emergence of magnetization plateaus as a function of the magnetic field, at $m_z = frac{1}{3}$ using 6- 9- and 12-site PEPS unit cells, and at $m_z = frac{1}{9}, frac{5}{9}$ and $frac{7}{9}$ using a 9-site PEPS unit cell, the later set-up being able to accommodate $sqrt{3} times sqrt{3}$ solid order. We also find that, at $m_z = frac{1}{3}$, (lattice) nematic and $sqrt{3} times sqrt{3}$ VBC-order states are degenerate within the accuracy of the 9-site simplex-method, for all anisotropy. The 6- and 12-site coarse-grained PEPS methods produce almost-degenerate nematic and $1 times 2$ VBC-Solid orders. Within our accuracy, the 6-site coarse-grained PEPS method gives slightly lower energies, which can be explained by the larger amount of entanglement this approach can handle, even when the PEPS unit-cell is not commensurate with the expected ground state. Furthermore, we do not observe chiral spin liquid behaviors at and close to the XY point, as has been recently proposed. Our results are the first tensor network investigations of the XXZ spin chain in a field, and reveal the subtle competition between nearby magnetic orders in numerical simulations of frustrated quantum antiferromagnets, as well as the delicate interplay between energy optimization and symmetry in tensor networks.
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