arXiv subjects

Shumpei Iino

Publications and source records attributed to Shumpei Iino.

5 recordsLinked to original sources

arXiv2021

Open spin chain realization of topological defect on 1d Ising model and boundary and bulk symmetry

We study the realizations of topological defects in 1d quantum Ising model with open boundary condition at criticality. Applying the construction discussed in [M. Hauru, G. Evenbly, W. W. Ho, D. Gaiotto, and G. Vidal, Phys. Rev. B 94, 115125 (2016)], we prove that the Ising model on an open chain with multiple topological defects can be transformed to the same model with boundary magnetic fields and noninteracting boundary degrees of freedom. This results in the appearance of linear combination of Cardy states [J. L. Cardy, Nucl. Phys. B 324, 581 (1989)], which can be interpreted as an edge state of the spin or fermion chain. We show that this edge state with the large boundary entropy can be protected under bulk perturbation whereas it is fragile to a boundary perturbation. Our formulation suggests an existence of nontrivial edge physics under the existence of topological defects and opens many interesting questions for future analysis related to boundary and bulk physics.

hep-th↗

arXiv2021

Boundary CFT and tensor network approach to surface critical phenomena of the tricritical 3-state Potts model

One-dimensional edges of classical systems in two dimension sometimes show surprisingly rich phase transitions and critical phenomena, particularly when the bulk is at criticality. As such a model, we study the surface critical behavior of the 3-state dilute Potts model whose bulk is tuned at the tricritical point. To investigate it more precisely than in the previous works [Y. Deng and H. W. J. Blöte, Phys. Rev. E 70, 035107(R) (2004); Phys. Rev. E 71, 026109 (2005)], we analyze it from the viewpoint of the boundary conformal field theory (BCFT). The complete classification of the conformal boundary conditions for the minimal BCFTs discussed in [R. E. Behrend et al., Nucl. Phys. B 579, 707 (2000)] allows us to collect the twelve boundary fixed points in the tricritical 3-state Potts BCFT. Employing the tensor network renormalization method, we numerically study the surface phase diagram of the tricritical 3-state Potts model in detail, and reveal that the eleven boundary fixed points among the twelve can be realized on the lattice by controlling the external field and coupling strength at the boundary. The last unfound fixed point would be out of the physically sound region in the parameter space, similarly to the `new' boundary condition in the 3-state Potts BCFT.

cond-mat.stat-mech↗

arXiv2020

Boundary conformal spectrum and surface critical behaviors of the classical spin systems: a tensor network renormalization study

We numerically obtain the conformal spectrum of several classical spin models on a two-dimensional lattice with open boundaries, for every boundary fixed point obtained by the Cardy's derivation [J. L. Cardy, Nucl. Phys. B 324, 581 (1989)]. In order to extract accurate conformal data, we implement the tensor network renormalization algorithm [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] extended so as to be applicable to a square lattice with open boundaries. We successfully compute the boundary conformal spectrum consistent with the underlying boundary conformal field theories (BCFTs) for the Ising, tri-critical Ising, and 3-state Potts models on the lattice, which allows us to confirm the validity of the BCFT analyses for the surface critical behaviors of those lattice models.

cond-mat.stat-mech↗

arXiv2019

Boundary Tensor Renormalization Group

We develop the tensor renormalization group (TRG) algorithm for statistical systems with open boundaries, which allows us to investigate not only the bulk but also the boundary property, such as the surface magnetization. We demonstrate that the tensors representing the boundary in our algorithm exhibit the fixed point structures just as bulk tensors in previous TRG algorithms. At criticality, the scale-invariant boundary fixed point tensors have the information of the conformal tower, which is described by the underlying boundary conformal field theory.

cond-mat.stat-mech↗

arXiv2019

Detecting signals of weakly first-order phase transitions in two-dimensional Potts models

We investigate the first-order phase transitions of the $q$-state Potts models with $q = 5, 6, 7$, and $8$ on the two-dimensional square lattice, using Monte Carlo simulations. At the very weakly first-order transition of the $q=5$ system, the standard data-collapse procedure for the order parameter, carried out with results for a broad range of system sizes, works deceptively well and produces non-trivial critical exponents different from the trivial values expected for first-order transitions. However, a more systematic study reveals significant drifts in the `pseudo-critical' exponents as a function of the system size. For this purpose, we employ two methods of analysis: the data-collapse procedure with narrow range of the system size, and the Binder-cumulant crossing technique for pairs of system sizes. In both methods, the estimates start to drift toward the trivial values as the system size used in the analysis exceeds a certain `cross-over' length scale. This length scale is remarkably smaller than the correlation length at the transition point for weakly first-order transitions, e.g., less than one tenth for $q=5$, in contrast to the naive expectation that the system size has to be comparable to or larger than the correlation length to observe the correct behavior. The results overall show that proper care is indispensable to diagnose the nature of a phase transition with limited system sizes.

cond-mat.stat-mech↗