arXiv subjects

Yoshiki Fukusumi

Publications and source records attributed to Yoshiki Fukusumi.

26 records · Page 2Linked 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

Kubo's response theory and bosonization with a background gauge field and irrelevant perturbations

Using conformal field theory calculations of the energy spectrum, within the XXZ model we investigate effects of the flux insertion and the Umklapp term. We discuss two approaches to the evaluation of the Drude weight, the first corresponding to the linear response theory and the second corresponding to the twisted boson theory with the Umklapp term. Divergences obtained in the context of the former contradict the Bethe ansatz results, with the two approaches coinciding for the free fermion point only. The origin of this discrepancy is in the different order in which the Umklapp term and the flux insertion are treated, where the marginal perturbation should be considered before the irrelevant. We calculate the scaling of the conductivity with system size and temperature in the long-wave limit.

cond-mat.stat-mech↗

arXiv2020

Spin interfaces and crossing probabilities of spin clusters in parafermionic models

We consider fractal curves in two-dimensional $Z_N$ spin lattice models. These are N states spin models that undergo a continuous ferromagnetic-paramagnetic phase transition described by the ZN parafermionic field theory. The main motivation here is to investigate the correspondence between Schramm-Loewner evolutions (SLE) and conformal field theories with extended conformal algebras (ECFT). By using Monte-Carlo simulation, we compute the fractal dimension of different spin interfaces for the N=3 and N=4 spin models that correspond respectively to the 3 states Potts model and to the Ashkin-Teller model at the Fateev-Zamolodchikov point. These numerical measures, that improve and complete the ones presented in the previous works, are shown to be consistent with SLE/ECFT predictions. We consider then the crossing probability of spin clusters in a rectangular domain. Using a multiple SLE approach, we provide crossing probability formulas for ZN parafarmionic theories. The parafermionic conformal blocks that enter the crossing probability formula are computed by solving a Knhiznik-Zamolodchikov system of rank 3. In the 3 states Potts model case, where the parafermionic blocks coincide with the Virasoro ones, we rederive the crossing formula found by S.M.Flores et al., that is in good agreement with our measures. For N>=4 where the crossing probability satisfies a third order differential equation instead of a second order one, our formulas are new. The theoretical predictions are compared to Monte-Carlo measures taken at N=4 and a fair agreement is found.

hep-th↗

arXiv2019

Bosonization with a background $U(1)$ gauge field

Bosonization is one of the most significant frameworks to analyze fermionic systems. In this work, we propose a new bosonization of Dirac fermion coupled with $U(1)$ background gauge field consistent with gauge invariance, global chiral anomaly matching and fermion-boson operator correspondence, either of which is not satisfied by previously developed bosonizations. The bilinear Dirac-mass term condensation paradox and its generalized form are resolved by our bosonization. This new bosonization approach to interacting systems also correctly captures the conformal characters of a significant class of critical lattice models, such as conformal dimensions and conformal anomaly of XXZ spin chain with twisted boundary condition. Our work clarifies the equivalence of fermionic flux insertion and bosonic background charge insertion for two-dimensional conformal field theory.

cond-mat.str-el↗

arXiv2018

Time reversing procedure of SLE and 2d gravity

We analyze the time reversing procedure of Schramm Loewner evolutions and its relation to Liouville field theory or 2d pure gravity. It enables one to obtain martingale observables by the calculation of Liouville field theory correlation functions.

math-ph↗

arXiv2018

Crossover of Correlation Functions near a Quantum Impurity in a Tomonaga-Luttinger Liquid

An impurity in a Tomonaga-Luttinger liquid leads to a crossover between short- and long-distance regime which describes many physical phenomena. However, calculation of the entire crossover of correlation functions over different length scales has been difficult. We develop a powerful numerical method based on infinite DMRG utilizing a finite system with infinite boundary conditions, which can be applied to correlation functions near an impurity. For the $S=1/2$ chain, we demonstrate that the full crossover can be precisely obtained, and that their limiting behaviors show a good agreement with field-theory predictions.

cond-mat.str-el↗

arXiv2018

Scaling of polarization amplitude in quantum many-body systems in one dimension

Resta proposed a definition of the electric polarization in one-dimensional systems in terms of the ground-state expectation value of the large gauge transformation operator. Vanishing of the expectation value in the thermodynamic limit implies that the system is a conductor. We study Resta's polarization amplitude (expectation value) in the $S=1/2$ XXZ chain and its several generalizations, in the gapless conducting Tomonaga-Luttinger Liquid phase. We obtain an analytical expression in the lowest-order perturbation theory about the free fermion point (XY chain), and an exact result for the Haldane-Shastry model with long-range interactions. We also obtain numerical results, mostly using the exact diagonalization method. We find that the amplitude exhibits a power-law scaling in the system size (chain length) and vanishes in the thermodynamic limit. On the other hand, the exponent depends on the model even when the low-energy limit is described by the Tomonaga-Luttinger Liquid with the same Luttinger parameter. We find that a change in the exponent occurs when the Umklapp term(s) are eliminated, suggesting the importance of the Umklapp terms.

cond-mat.stat-mech↗

arXiv2017

Multiple Schramm-Loewner evolutions for coset Wess-Zumino-Witten models

We formulate multiple Schramm-Loewner evolutions (SLEs) for coset Wess-Zumino-Witten (WZW) models. The resultant SLEs may describe the critical behavior of multiple interfaces for the 2D statistical mechanics models whose critical properties are classified by coset WZW models. The SLEs are essentially characterized by multiple Brownian motions on a Lie group manifold as well as those on the real axis. The drift terms of the Brownian motions, which come from interactions of interfaces, are explicitly determined by imposing a martingale condition on correlation functions among boundary condition changing operators. As a concrete example, we formulate multiple SLE on the $Z(n)$ parafermion model and calculate the crossing probability which is closely related to 3-SLE drift terms.

math-ph↗