arXiv subjects

Keisuke Totsuka

Publications and source records attributed to Keisuke Totsuka.

At least 19 recordsLinked to original sources

arXiv2024

Infrared properties of two-dimensional $\mathrm{SU}(N)/H$ nonlinear $\sigma$ models at nonzero $\theta$ angles

A general strategy is proposed to explore the low-energy properties of two-dimensional nonlinear $\sigma$ models with $\theta$ terms. We demonstrate its application to nonlinear $\sigma$ models with the target space $\text{SU($N$)}$/H, which include $\mathbb{C}P^{N-1}$, complex Grassmannian manifolds as well as the flag $\text{SU($N$)}/\text{U(1)}^{N-1}$ and $\text{SU($N$)})/\text{SO($N$)}$ manifolds. By analyzing the symmetry and its anomaly content, we realize these nonlinear $\sigma$ models through perturbations added to the SU(N)$_1$ conformal field theory. For the flag-manifold $\text{SU($N$)}/\text{U(1)}^{N-1}$ and $\text{SU($N$)})/\text{SO($N$)}$ models, those perturbations are shown to correspond to the marginal current-current operator with the specific sign which leads to a massless renormalization group flow to the SU(N)$_1$ fixed point. In contrast, a massive regime with a two-fold ground-state degeneracy is found for the $\mathbb{C}P^{N-1}$ ($N >2$) and Grassmannian nonlinear $\sigma$ models at $\theta=\pi$.

cond-mat.str-el↗

arXiv2024

Emergent spacetime supersymmetry in an interacting Kitaev chain with explicit supersymmetry

We investigate the emergence of spacetime supersymmetry (SUSY) in an interacting Kitaev chain model with explicit microscopic $\mathcal{N}=1$ quantum mechanical SUSY. As the interaction strength is varied, the model transitions from a weak-coupling gapless phase with spontaneously broken SUSY to a strong-coupling phase with restored SUSY. In this paper, we numerically determine the transition point and investigate the phase structure around it. The weak-coupling phase is governed by the Ising conformal field theory (CFT) with central charge $c=1/2$, which agrees with the prediction made in our previous paper. At the SUSY restoration transition, which borders the strong-coupling gapped phase, the transition belongs to the $c=7/10$ tricritical Ising universality with emergent superconformal invariance. Crucially, the phase structure around the transition closely aligns with the scenario proposed by Zamolodchikov and others based on the integrable deformation of CFTs. These findings provide a concrete example of a lattice model where explicit microscopic supersymmetry at criticality enriches the understanding of phase transitions governed by supersymmetric conformal field theories.

cond-mat.str-el↗

arXiv2024

Non-Landau quantum phase transition in modulated SU(N) Heisenberg spin chains

We investigate the nature of the quantum phase transition in modulated SU(N) Heisenberg spin chains. In the odd-N case, the transition separates a trivial non-degenerate phase to a doubly-degenerate gapped chiral PSU(N) symmetry-protected topological (SPT) phase which breaks spontaneously the inversion symmetry. The transition is not an Ising transition associated to the breaking of the $\mathbb{Z}_2$ inversion symmetry, but is governed by the delocalization of the edge states of the SPT phase. In this respect, a modulated SU(N) Heisenberg spin chain provides a simple example in one dimension of a non-Landau phase transition which is described by the SU(N)$_1$ conformal field theory. We show that the chiral SPT phase exhibits fractionalized spinon excitations, which can be confined by changing the model parameters slightly.

cond-mat.str-el↗

arXiv2024

Computational Characterization of Symmetry-Protected Topological Phases in Open Quantum Systems

It is a challenging problem to correctly characterize the symmetry-protected topological (SPT) phases in open quantum systems. As the measurement-based quantum computation (MBQC) utilizes non-trivial edge states of the SPT phases as the logical qubit, its computational power is closely tied to the non-trivial topological nature of the phases. In this paper, we propose to use the gate fidelity which is a measure of the computational power of the MBQC to identify the SPT phases in mixed-state settings. Specifically, we investigate the robustness of the Haldane phase by considering the MBQC on the Affleck-Kennedy-Lieb-Tasaki state subject to different types of noises. To illustrate how our criterion works, we analytically and numerically calculated the gate fidelity to find that its behavior depends crucially on whether the noises satisfy a certain symmetry condition with respect to the on-site $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry. In particular, the fidelity for the identity gate, which is given by the sum of the non-local string order parameters, plays an important role. Furthermore, we demonstrate that a stronger symmetry conditions are required to be able to perform other (e.g., the $Z$-rotation gate) gates with high fidelity. By examining which unitary gates can be implemented with the MBQC on the decohered states, we can gain a useful insight into the richer structure of noisy SPT states that cannot be captured solely by the string order parameters.

quant-ph↗

arXiv2024

Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU($N$) Kondo lattice model

The nature of the insulating phases of the SU($N$)-generalization of the one-dimensional Kondo lattice model is investigated by means of non-perturbative approaches. By extending the Lieb-Schultz-Mattis (LSM) argument to multi-component fermion systems with translation and global SU($N$) symmetries, we derive two indices which depend on the filling and the ``SU($N$)-spin'' (representation) of the local moments. These indices strongly constrain possible insulating phases; for instance, when the local moments transform in the $N$-dimensional (defining) representation of SU($N$), a featureless Kondo insulator is possible only at filling $f= 1-1/N$. To obtain further insight into the insulating phases suggested by the LSM argument, we derive low-energy effective theories by adding an antiferromagnetic Heisenberg exchange interaction among the local moments [the SU($N$) Kondo-Heisenberg model]. A conjectured global phase diagram of the SU($N$) Kondo lattice model as a function of the filling and the Kondo coupling is then obtained by a combination of different analytical approaches.

cond-mat.str-el↗

arXiv2023

Interacting Kitaev Chain with $\mathcal{N}=1$ Supersymmetry

Lattice models with supersymmetry are known to exhibit a variety of remarkable properties that do not exist in the relativistic models. In this paper, we introduce an interacting generalization of the Kitaev chain of Majorana fermions with $\mathcal{N} = 1$ supersymmetry and investigate its low-energy properties, paying particular attention to the ground-state degeneracy and low-lying fermionic excitations. First, we establish the existence of a phase with spontaneously broken supersymmetry and a phase transition out of it with the help of variational arguments and the exact ground state. We then develop, based on the superfield formalism, a simple mean-field theory, in which the order parameters detect supersymmetry-breaking, to understand the ground-state phases and low-lying Nambu-Goldstone fermions. At the solvable point ({\em frustration-free point}), the exact ground state of an open chain exhibits large degeneracy of the order of the system size, which is attributed to the existence of a zero-energy domain wall (dubbed kink or skink) separating the topological and trivial states of Majorana fermions. Our results may shed new light on the intriguing ground-state properties of supersymmetric lattice models.

cond-mat.str-el↗

arXiv2023

Supersymmetry Breaking in a Generalized Nicolai Model with Fermion Pairing

We introduce a supersymmetric lattice fermion model that contains both fermion pairing and the interacting Nicolai model. This model possesses a single control parameter, $g$, introduced through the anticommutator of the supersymmetry generators (supercharge), and it is shown that supersymmetry is broken in both finite and infinite systems as long as $g$ is finite. Additionally, the single-mode approximation is employed to establish an upper bound on the dispersion relation of Nambu-Goldstone (NG) fermions, demonstrating their gaplessness. Finally, it is shown, through numerical and analytic calculations, that the anticipated extensive ground-state degeneracy and a zero-energy flat band does not occur for generic values of the parameter $g$.

cond-mat.str-el↗

arXiv2023

Ferromagnetism in the SU(N) Kondo lattice model -- SU(N) double exchange and supersymmetry

We study the ground-state properties of the SU(N)-generalization of the Kondo-lattice model in one dimension when the Kondo coupling J_K (both ferromagnetic and antiferromagnetic) is sufficiently strong. Both cases can be realized using alkaline-earth-like cold gases in optical lattices. Specifically, we first carry out the strong-coupling expansion and identify two insulating phases (one of which is the SU(N)-analogue of the well-known gapped Kondo singlet phase). We then rigorously establish that the ground state in the low-density (for J_K<0) or the high-density (for J_K>0) region is ferromagnetic. The results are accounted for by generalizing the double-exchange mechanism to SU(N) "spins". Possible realizations of Bose-Fermi supersymmetry SU(N|1) in the (generalized) SU(N) Kondo-lattice model are discussed as well.

cond-mat.str-el↗

arXiv2022

Electric and Magnetic Properties of Higher-Spin Kondo-Heisenberg Models at Strong Coupling

We study higher-spin ($S \geq 1$) generalization of the one-dimensional Kondo-Heisenberg model, in which the local spin-$S$ moments of the Kondo lattice model interact with each other via the antiferromagnetic Heisenberg interaction ($J_{\text{H}}$), by analytical and numerical methods. The strong-coupling (i.e., large Kondo-coupling) expansion maps out an insulating phase at half-filling whose magnetic correlation depends on the parity of $2S$ as well as a ferromagnetic metallic phase which dominates the strong-coupling region at generic fillings. Then, we carried out the Density-Matrix Renormalization Group (DMRG) simulations for $S=1$ to closely investigate the phase structure at large but finite Kondo coupling. At half-filling, the Kondo coupling and $J_{\text{H}}$ do not compete and the insulating spin-gapless phase is stable, while the competition of the two leads to a stepwise collapse of the strong-coupling ferromagnetism via an intervening dimerized insulating phase with power-law spin correlation at quarter-filling.

cond-mat.str-el↗

arXiv2021

Abelian SU$(N)_1$ Chiral Spin Liquids on the Square Lattice

In the physics of the Fractional Quantum Hall (FQH) effect, a zoo of Abelian topological phases can be obtained by varying the magnetic field. Aiming to reach the same phenomenology in spin-like systems, we propose a family of SU($N$)-symmetric models in the fundamental representation, on the square lattice with short-range interactions restricted to triangular units, a natural generalization for arbitrary $N$ of an SU($3$) model studied previously where time-reversal symmetry is broken explicitly. Guided by the recent discovery of SU($2$)$_1$ and SU($3$)$_1$ chiral spin liquids (CSL) on similar models we search for topological SU($N$)$_1$ CSL in some range of the Hamiltonian parameters via a combination of complementary numerical methods such as exact diagonalizations (ED), infinite density matrix renormalization group (iDMRG) and infinite Projected Entangled Pair State (iPEPS). Extensive ED on small (periodic and open) clusters up to $N=10$ and an innovative SU($N$)-symmetric version of iDMRG to compute entanglement spectra on (infinitely-long) cylinders in all topological sectors provide unambiguous signatures of the SU($N$)$_1$ character of the chiral liquids. An SU($4$)-symmetric chiral PEPS, constructed in a manner similar to its SU($2$) and SU($3$) analogs, is shown to give a good variational ansatz of the $N=4$ ground state, with chiral edge modes originating from the PEPS holographic bulk-edge correspondence. Finally, we discuss the possible observation of such Abelian CSL in ultracold atom setups where the possibility of varying $N$ provides a tuning parameter similar to the magnetic field in the physics of the FQH effect.

cond-mat.str-el↗

arXiv2019

Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins

Chiral Haldane phases are examples of one-dimensional topological states of matter which are protected by projective SU($N$) group (or its subgroup $\mathbb{Z}_N \times \mathbb{Z}_N$) with $N>2$. The unique feature of these symmetry protected topological (SPT) phases is that they are accompanied by inversion-symmetry breaking and the emergence of different left and right edge states which transform, for instance, respectively in the fundamental ($\boldsymbol{N}$) and anti-fundamental ($\overline{\boldsymbol{N}}$) representations of SU($N$). We show, by means of complementary analytical and numerical approaches, that these chiral SPT phases as well as the non-chiral ones are realized as the ground states of a generalized two-leg SU($N$) spin ladder in which the spins in the first chain transform in $\boldsymbol{N}$ and the second in $\overline{\boldsymbol{N}}$. In particular, we map out the phase diagram for $N=3$ and $4$ to show that {\em all} the possible symmetry-protected topological phases with projective SU($N$)-symmetry appear in this simple ladder model.

cond-mat.str-el↗

arXiv2019

Non-Abelian Aharonov-Casher Phase Factor in Mesoscopic Systems

The matrix-valued Aharonov-Casher phase factor $F_{\text{AC}}$ (related to the c-number Aharonov-Casher phase $λ_{\text{AC}}$) plays an important role in the physics of mesoscopic systems in which spin-orbit coupling is relevant. Yet, its relation to experimental observables is rather elusive. Based on the SU(2)-gauge-invariant formulation of the Schroedinger equation, we relate $F_{\text{AC}}$ to measurable quantities in electronic interferometers subject to electric fields that generate Rashba or Dresselhaus spin-orbit coupling. Specifically, we consider electron transmission through (i) a single-channel ring interferometer and (ii) a two-channel square interferometer. In both examples, we derive the closed expressions of the conductance and show them to be simple rational functions of the traceful part of $F_{\text{AC}}$. In the second case, we also derive a closed expression for the electron spin polarization vector and find it to be a simple function of both the traceful and traceless parts of $F_{\text{AC}}$. This analysis then suggests a direct way for an experimental access to this elusive quantity.

cond-mat.mes-hall↗

arXiv2016

Topological quantum phase transitions in a Majorana chain with spatial modulation

We numerically study the quantum phase transitions and the stability of Majorana zero modes in a generalized Kitaev model in one dimension when the chemical potential is periodically modulating in space. By using the exact diagonalization method for open boundary condition, we investigate the ground-state phases in terms of the non-local properties such as the entanglement spectrum (ES) and the string correlation functions. When we vary the phase of the modulation, the number of the Majorana zero modes changes, which manifests itself in the degeneracy of the lowest level of the ES. Next, we study the quantum phase transitions driven by the change in the amplitude of the modulation. In particular, for certain values of the wave number and the phase of the modulation, we observe a quantum phase transition from one topological phase into another where the string correlation function oscillates in space. We also show a case where the degeneracy of the ES does not change even for large enough amplitude of the modulation. Finally, we characterize the phases of the system with periodic boundary condition by the topological invariant, which reflects the number of the zero-energy excitations.

cond-mat.stat-mech↗

arXiv2016

Bulk effective theory in coupled wire construction from generalized Wilson line

We reconsider the coupled wire construction, which is a useful method of obtaining two and three-dimensional topologically ordered states from an array of one-dimensional CFTs, and show that there is the hidden structure in the bulk of the constructed model. In order to uncover the structure hidden in the gapped bulk, we introduce a generalized Wilson line and show the necessity of introducing a new gauge field, which behaves like the Chern-Simons gauge field. From these examination, it is possible to show that in this formulation the bulk theory is the U(1) Chern-Simons gauge theory and the edge theory is the chiral Luttinger theory. We explicitly demonstrate our method for the Laughlin states and the chiral spin liquid state.

cond-mat.str-el↗

arXiv2016

Topological and dynamical properties of a generalized cluster model in one dimension

We study the ground-state phase diagram and dynamics of the one-dimensional cluster model with several competing interactions. Paying particular attention to the relation between the entanglement spectrum (ES) and the bulk topological (winding) number, we first map out the ground-state phases of the model and determine the universality classes of the transitions from the exact solution. We then investigate the dynamical properties during interaction sweeps through the critical points of topological phase transitions. When the sweep speed is slow, the correlation functions and the entanglement entropy exhibit spatially periodic structures. On top of this, the levels in the ES oscillate temporally during the dynamics. By explicitly calculating the above quantities for excited states, we attribute these behaviors to the Bogoliubov quasiparticles generated near the critical points. We also show that the ES reflects the strength of the Majorana correlation even for the excited states.

cond-mat.stat-mech↗

arXiv2015

Density-Matrix Renormalization Group Study of Kitaev--Heisenberg Model on a Triangular Lattice

We study the Kitaev--Heisenberg model on a triangular lattice by using the two-dimensional density-matrix renormalization group method. Calculating the ground-state energy and spin structure factors, we obtain a ground-state phase diagram of the Kitaev--Heisenberg model. As suggested by previous studies, we find a 120$^\circ$ antiferromagnetic (AFM) phase, a $\mathbb{Z}_2$-vortex crystal phase, a nematic phase, a dual $\mathbb{Z}_2$-vortex crystal phase (the dual counterpart of the $\mathbb{Z}_2$-vortex crystal phase), a $\mathbb{Z}_6$ ferromagnetic phase, and a dual ferromagnetic phase (the dual counterpart of the $\mathbb{Z}_6 $ ferromagnetic phase). Spin correlations discontinuously change at phase boundaries because of first-order phase transitions. We also study the relation among the von Neumann entanglement entropy, entanglement spectrum, and phase transitions of the model. We find that the Schmidt gap closes at phase boundaries and thus the entanglement entropy clearly changes as well. This is different from the Kitaev--Heisenberg model on a honeycomb lattice, where the Schmidt gap and entanglement entropy are not necessarily a good measure of phase transitions.

cond-mat.str-el↗

arXiv2015

Symmetry-protected topological order in magnetization plateau states of quantum spin chains

A symmetry-protected topologically ordered phase is a short-range entangled state, for which some imposed symmetry prohibits the adiabatic deformation into a trivial state which lacks entanglement. In this paper we argue that magnetization plateau states of one-dimensional antiferromagnets which satisfy the conditions $S-m\in$ odd integer, where $S$ is the spin quantum number and $m$ the magnetization per site, can be identified as symmetry-protected topological states if an inversion symmetry about the link center is present. This assertion is reached by mapping the antiferromagnet into a nonlinear sigma model type effective field theory containing a novel Berry phase term (a total derivative term) with a coefficient proportional to the quantity $S-m$, and then analyzing the topological structure of the ground state wave functional which is inherited from the latter term. A boson-vortex duality transformation is employed to examine the topological stability of the ground state in the absence/presence of a perturbation violating link-center inversion symmetry. Our prediction based on field theories is verified by means of a numerical study of the entanglement spectra of actual spin chains, which we find to exhibit twofold degeneracies when the aforementioned condition is met. We complete this study with a rigorous analysis using matrix product states.

cond-mat.str-el↗

arXiv2015

Phase diagram and sweep dynamics of a one-dimensional generalized cluster model

We numerically study quantum phase transitions and dynamical properties in the one-dimensional cluster model with several interactions by using the time-evolving block decimation method for infinite systems and the exact diagonalization. First, boundaries among several quantum phases of the model are determined from energy gap and each phase is characterized by order parameters and the entanglement spectrum (ES). We confirm that in the model with open boundary condition the degeneracy of the lowest levels in the ES corresponds to that of the ground states. Then, using the time-dependent Bogoliubov transformation with open boundary condition, we investigate dynamical properties during an interaction sweep through the critical point which separates two topological phases involving four-fold degeneracy in the ground state. After a slow sweep across the critical point, we observe spatially periodic structures in the string correlation functions and the entanglement entropy. It is shown that the periodicities stem from the Bogoliubov quasiparticles generated near the critical point.

cond-mat.stat-mech↗