57 research outputs found
Latent Heat Calculation of the 3D q=3, 4, and 5 Potts models by Tensor Product Variational Approach
Three-dimensional (3D) -state Potts models (=3, 4, and 5) are studied
by the tensor product variational approach (TPVA), which is a recently
developed variational method for 3D classical lattice models. The variational
state is given by a two-dimensional (2D) product of local factors, and is
improved by way of self-consistent calculations assisted by the corner transfer
matrix renormalization group (CTMRG). It should be noted that no a priori
condition is imposed for the local factor. Transition temperatures and latent
heats are calculated from the observations of thermodynamic functions in both
ordered and disordered phases.Comment: RevTeX4 format, 7 pages, 15 figures, submitted to Phys. Rev.
Area-Law Study of Quantum Spin System on Hyperbolic Lattice Geometries
Magnetic properties of the transverse-field Ising model on curved
(hyperbolic) lattices are studied by a tensor product variational formulation
that we have generalized for this purpose. First, we identify the quantum phase
transition for each hyperbolic lattice by calculating the magnetization. We
study the entanglement entropy at the phase transition in order to analyze the
correlations of various subsystems located at the center with the rest of the
lattice. We confirm that the entanglement entropy satisfies the area law at the
phase transition for fixed coordination number, i.e., it scales linearly with
the increasing size of the subsystems. On the other hand, the entanglement
entropy decreases as power-law with respect to the increasing coordination
number.Comment: accepted in Acta Phys. Pol. A (2020
Phase diagram of the 3D Axial-Next-Nearest-Neighbor Ising model
The three-dimensional axial-next-nearest-neighbor Ising (ANNNI) model is
studied by a modified tensor product variational approach (TPVA). A global
phase diagram is constructed with numerous commensurate and incommensurate
magnetic structures. The devil's stairs behavior for the model is confirmed.
The wavelength of the spin modulated phases increases to infinity at the
boundary with the ferromagnetic phase. Widths of the commensurate phases are
considerably narrower than those calculated by mean-field approximations.Comment: 8 pages, 12 figures, RevTeX4 forma
Absence of logarithmic divergence of the entanglement entropies at the phase transitions of a 2D classical hard rod model
Entanglement entropy is a powerful tool to detect continuous, discontinuous
and even topological phase transitions in quantum as well as classical systems.
In this work, von Neumann and Renyi entanglement entropies are studied
numerically for classical lattice models in a square geometry. A cut is made
from the center of the square to the midpoint of one of its edges, say the
right edge. The entanglement entropies measure the entanglement between the
left and right halves of the system. As in the strip geometry, von Neumann and
Renyi entanglement entropies diverge logarithmically at the transition point
while they display a jump for first-order phase transitions. The analysis is
extended to a classical model of non-overlapping finite hard rods deposited on
a square lattice for which Monte Carlo simulations have shown that, when the
hard rods span over 7 or more lattice sites, a nematic phase appears in the
phase diagram between two disordered phases. A new Corner Transfer Matrix
Renormalization Group algorithm (CTMRG) is introduced to study this model. No
logarithmic divergence of entanglement entropies is observed at the phase
transitions in the CTMRG calculation discussed here. We therefore infer that
the transitions neither can belong to the Ising universality class, as
previously assumed in the literature, nor be discontinuous
Spherical Deformation for One-dimensional Quantum Systems
System-size dependence of the ground-state energy E^N is investigated for
N-site one-dimensional (1D) quantum systems with open boundary condition, where
the interaction strength decreases towards the both ends of the system. For the
spinless Fermions on the 1D lattice we have considered, it is shown that the
finite-size correction to the energy per site, which is defined as E^N / N -
\lim_{N \to \infty} E^N / N, is of the order of 1 / N^2 when the reduction
factor of the interaction is expressed by a sinusoidal function. We discuss the
origin of this fast convergence from the view point of the spherical geometry.Comment: 16 pages, 8 figures, the paper includes Errat
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