arXiv subjects

Soichiro Shimamori

Publications and source records attributed to Soichiro Shimamori.

13 recordsLinked to original sources

arXiv2026

Detecting one-dimensional bosonic SPT phases via twisted entropic order parameter

Entanglement asymmetry, introduced by F. Ares, S. Murciano and P. Calabrese, provides a density-matrix diagnostic of symmetry breaking and successfully captures the Landau data associated with a broken symmetry pattern. However, it is by now well established that gapped quantum many-body systems can exhibit phases which are not characterized solely by Landau symmetry breaking. A fundamental example is a symmetry-protected topological (SPT) phase, and the ordinary definition of entanglement asymmetry is insensitive to this topological information. In this work we introduce a refined quantity, which we call the twisted entropic order parameter, designed to detect SPT phases from reduced density matrices, particularly focusing on one-dimensional bosonic systems. The key ingredient in our construction is an ancilla degrees of freedom that coherently records the untwisted state and the twisted state associated to a one-ended topological defect of unbroken symmetry, so that the enlarged density matrix retains the charge carried by the defect endpoint. We demonstrate our proposal in concrete lattice models and further generalize it beyond ordinary group symmetries, establishing its ability to diagnose SPT phases. This provides a first step toward a unified entanglement-asymmetry framework for diagnosing quantum phases of matter.

hep-th↗

arXiv2026

Entanglement Asymmetry and Quantum Mpemba Effect for Non-Abelian Global Symmetry

Entanglement asymmetry is a measure that quantifies the degree of symmetry breaking at the level of a subsystem. In this work, we investigate the entanglement asymmetry in $\widehat{su}(N)_k$ Wess-Zumino-Witten model and discuss the quantum Mpemba effect for SU$(N)$ symmetry, the phenomenon that the more symmetry is initially broken, the faster it is restored. Due to the Coleman-Mermin-Wagner theorem, spontaneous breaking of continuous global symmetries is forbidden in $1+1$ dimensions. To circumvent this no-go theorem, we consider excited initial states which explicitly break non-Abelian global symmetry. We particularly focus on the initial states built from primary operators in the fundamental and adjoint representations. In both cases, we study the real-time dynamics of the Rényi entanglement asymmetry and provide clear evidence of quantum Mpemba effect for SU$(N)$ symmetry. Furthermore, we find a new type of quantum Mpemba effect for the primary operator in the fundamental representation: increasing the rank $N$ leads to stronger initial symmetry breaking but faster symmetry restoration. Also, increasing the level $k$ leads to weaker initial symmetry breaking but slower symmetry restoration. On the other hand, no such behavior is observed for adjoint case, which may suggest that this new type of quantum Mpemba effect is not universal.

hep-th↗

arXiv2026

The SymTFT for $N$-ality defects: Part I

In order to obtain the SymTFT for a theory with an $N$-ality extension of a discrete, Abelian group $G$, one begins by considering a bulk $G$-gauge theory, and then gauges an appropriate $\mathbb{Z}_N$ symmetry. This procedure involves three choices: the choice of a suitable bulk $\mathbb{Z}_N$ symmetry, of a fractionalization class, and of a discrete torsion. The first choice is, somewhat surprisingly, the most involved, and in this paper we discuss it in detail. In particular, we show that the choice of bulk $\mathbb{Z}_N$ symmetry determines all boundary $F$-symbols with a single incoming $N$-ality defect, and that any theory with an $N$-ality symmetry is invariant under a certain twisted gauging given in terms of these $F$-symbols. These $F$-symbols can furthermore be input into the pentagon identities to obtain the other $F$-symbols, up to freedoms related to the choices appearing in the second and third steps of bulk gauging. Although many of our results hold for general $N$, we restrict ourselves in some places to the case of $N=p$ prime. In particular, for generic triality defects, we acquire explicit $F$-symbols which are reminiscent of those in Tambara-Yamagami fusion categories.

hep-th↗

arXiv2025

Localized RG flows on composite defects and $\mathcal{C}$-theorem

We consider a composite defect system where a lower-dimensional defect (sub-defect) is embedded to a higher-dimensional one, and examine renormalization group (RG) flows localized on the defect. A composite defect is constructed in the $(3-ε)$-dimensional free $\text{O}(N)$ vector model with line and surface interactions by triggering localized RG flows to non-trivial IR fixed points. Focusing on the case where the symmetry group $\text{O}(N)$ is broken to a subgroup $\text{O}(m)\times\text{O}(N-m)$ on the line defect, there is an $\text{O}(N)$ symmetric fixed point for all $N$, while two additional $\text{O}(N)$ symmetry breaking ones appear for $N\ge 23$. We also examine a $\mathcal{C}$-theorem for localized RG flows along the sub-defect and show that the $\mathcal{C}$-theorem holds in our model by perturbative calculations.

hep-th↗

arXiv2025

Subdimensional Disorder and Logarithmic Defect

We study quenched disorder localized on a $p$-dimensional subspacetime in a $d$-dimensional conformal field theory. Motivated by the logarithmic behavior often associated with disorder, we introduce a defect setup in which bulk local operators transform in ordinary conformal representations, while defect local operators assemble into logarithmic multiplets. We refer to such objects as logarithmic defects and investigate their model-independent properties dictated solely by conformal symmetry and its representation theory, including correlation functions, logarithmic defect operator expansions, and conformal blocks. As a concrete example, we analyze the free scalar theory with a generalized pinning defect subject to random coupling fluctuations, and we identify a half-line of fixed points describing the corresponding logarithmic conformal defects. Along the way, we propose a candidate monotone governing defect renormalization group flows induced by subdimensional disorder. We comment on various generalizations and the broader program of bootstrapping logarithmic defects.

hep-th↗

arXiv2025

Boundary Scattering and Non-invertible Symmetries in 1+1 Dimensions

Recent studies by Copetti, Córdova and Komatsu have revealed that when non-invertible symmetries are spontaneously broken, the conventional crossing relation of the S-matrix is modified by the effects of the corresponding topological quantum field theory (TQFT). In this paper, we extend these considerations to $(1+1)$-dimensional quantum field theories (QFTs) with boundaries. In the presence of a boundary, one can define not only the bulk S-matrix but also the boundary S-matrix, which is subject to a consistency condition known as the boundary crossing relation. We show that when the boundary is weakly-symmetric under the non-invertible symmetry, the conventional boundary crossing relation also receives a modification due to the TQFT effects. As a concrete example of the boundary scattering, we analyze kink scattering in the gapped theory obtained from the $Φ_{(1,3)}$-deformation of a minimal model. We explicitly construct the boundary S-matrix that satisfies the Ward-Takahashi identities associated with non-invertible symmetries.

hep-th↗

arXiv2024

New Field Theories with Foliation Structure and Subdimensional Particles from Godbillon-Vey Invariant

Recently, subdimensional particles including fractons have attracted much attention from various areas. Notable features of such matter phases are mobility constraints and subextensive ground state degeneracies (GSDs). In this paper, we propose a BF-like theory motivated by the Godbillon-Vey invariant, which is a mathematical invariant of the foliated manifold. Our theory hosts subsystem higher form symmetries which manifestly ensure the mobility constraint and subextensive GSD through the spontaneous symmetry breaking. We also discuss some lattice spin models which realize the same low energy behaviours as the BF-like theory. Furthermore, we explore dynamical matter theories which are coupled to the BF-like theory.

hep-th↗

arXiv2024

Conformal field theory with composite defect

We explore higher-dimensional conformal field theories (CFTs) in the presence of a conformal defect that itself hosts another sub-dimensional defect. We refer to this new kind of conformal defect as the composite defect. We elaborate on the various conformal properties of the composite defect CFTs, including correlation functions, operator expansions, and conformal block expansions. As an example, we present a free O(N) vector model in the presence of a composite defect. Assuming the averaged null energy condition (ANEC) does hold even for the defect systems, we conclude that some boundary conditions can be excluded. Our investigations shed light on the rich phenomenology arising from hierarchical defect structures, paving the way for a deeper understanding of critical phenomena in nature.

hep-th↗

arXiv2024

Non-invertible duality defect and non-commutative fusion algebra

We study non-invertible duality symmetries by gauging a diagonal subgroup of a non-anomalous U(1) $\times$ U(1) global symmetry. In particular, we employ the half-space gauging to $c=2$ bosonic torus conformal field theory (CFT) in two dimensions and pure U(1) $\times$ U(1) gauge theory in four dimensions. In $c=2$ bosonic torus CFT, we show that the non-invertible symmetry obtained from the diagonal gauging becomes emergent on an irrational CFT point. We also calculate the fusion rules concerning the duality defect. We find out that the fusion algebra is non-commutative. We also obtain a similar result in pure U(1) $\times$ U(1) gauge theory in four dimensions.

hep-th↗

arXiv2023

Entanglement Rényi entropy and boson-fermion duality in massless Thirring model

We investigate the second Rényi entropy of two intervals in the massless Thirring model describing a self-interacting Dirac fermion in two dimensions. Boson-fermion duality relating this model to a free compact boson theory enables us to simplify the calculation of the second Rényi entropy, reducing it to the evaluation of the partition functions of the bosonic theory on a torus. We derive exact results on the second Rényi entropy, and examine the dependence on the sizes of the intervals and the coupling constant of the model both analytically and numerically. We also explore the mutual Rényi information, a measure quantifying the correlation between the two intervals, and find that it generally increases as the coupling constant of the Thirring model becomes larger.

hep-th↗

arXiv2023

Comments on epsilon expansion of the O$(N)$ model with boundary

The O$(N)$ vector model in the presence of a boundary has a non-trivial fixed point in $(4-ε)$ dimensions and exhibits critical behaviors described by boundary conformal field theory. The spectrum of boundary operators is investigated at the leading order in the $ε$-expansion by diagrammatic and axiomatic approaches. In the latter, we extend the framework of Rychkov and Tan for the bulk theory to the case with a boundary and calculate the conformal dimensions of boundary composite operators with attention to the analyticity of correlation functions. In both approaches, we obtain consistent results.

hep-th↗

arXiv2023

The epsilon expansion of the O$(N)$ model with line defect from conformal field theory

We employ the axiomatic framework of Rychkov and Tan to investigate the critical O$(N)$ vector model with a line defect in $(4-ε)$ dimensions. We assume the fixed point is described by defect conformal field theory and show that the critical value of the defect coupling to the bulk field is uniquely fixed without resorting to diagrammatic calculations. We also study various defect localized operators by the axiomatic method, where the analyticity of correlation functions plays a crucial role in determining the conformal dimensions of defect composite operators. In all cases, including operators with operator mixing, we reproduce the leading anomalous dimensions obtained by perturbative calculations.

hep-th↗

arXiv2022

Method of images in defect conformal field theories

We propose a prescription for describing correlation functions in higher-dimensional defect conformal field theories (DCFTs) by those in ancillary conformal field theories (CFTs) without defects, which is a vast generalization of the image method in two-dimensional boundary CFTs. A correlation function of $n$ operators inserted away from a defect in a DCFT is represented by a correlation function of $2n$ operators in the ancillary CFT, each pair of which is placed symmetrically with respect to the defect. For scalar operators, we establish the correspondence by matching the constraints on correlation functions imposed by conformal symmetry on both sides. Our method has potential to shed light on new aspects of DCFTs from the viewpoint of conventional CFTs.

hep-th↗