arXiv subjects

Hosho Katsura

Publications and source records attributed to Hosho Katsura.

At least 91 records · Page 5Linked to original sources

arXiv2017

Zero-energy states in conformal field theory with sine-square deformation

We study the properties of two-dimensional conformal field theories (CFTs) with sine-square deformation (SSD). We show that there are no eigenstates of finite norm for the Hamiltonian of a unitary CFT with SSD, except for the zero-energy vacuum state $|0\rangle$. We then introduce a regularized version of the SSD Hamiltonian which is related to the undeformed Hamiltonian via a unitary transformation corresponding to the Mobius quantization. The unitary equivalence of the two Hamiltonians allows us to obtain zero-energy states of the deformed Hamiltonian in a systematic way. The regularization also provides a way to compute the expectation values of observables in zero-energy states that are not necessarily normalizable.

cond-mat.stat-mech↗

arXiv2017

A New Numerical Method for $\mathbb{Z}_2$ Topological Insulators with Strong Disorder

We propose a new method to numerically compute the $\mathbb{Z}_2$ indices for disordered topological insulators in Kitaev's periodic table. All of the $\mathbb{Z}_2$ indices are known to be derived from the index formulae which are expressed in terms of a pair of projections introduced by Avron, Seiler, and Simon. For a given pair of projections, the corresponding index is determined by the spectrum of the difference between the two projections. This difference exhibits remarkable and useful properties, as it is compact and has a supersymmetric structure in the spectrum. These properties make it possible to numerically determine the indices of disordered topological insulators highly efficiently. The method is demonstrated for the Bernevig-Hughes-Zhang and Wilson-Dirac models whose topological phases are characterized by a $\mathbb{Z}_2$ index in two and three dimensions, respectively.

cond-mat.mes-hall↗

arXiv2017

Finite-size Gap, Magnetization, and Entanglement of Deformed Fredkin Spin Chain

We investigate ground- and excited-state properties of the deformed Fredkin spin chain proposed by Salberger, Zhang, Klich, Korepin, and the authors. This model is a one-parameter deformation of the Fredkin spin chain, whose Hamiltonian is $3$-local and translationally invariant in the bulk. The model is frustration-free and its unique ground state can be expressed as a weighted superposition of colored Dyck paths. We focus on the case where the deformation parameter $t>1$. By using a variational method, we prove that the finite-size gap decays at least exponentially with increasing the system size. We prove that the magnetization in the ground state is along the $z$-direction, namely $\langle s^x \rangle =\langle s^y \rangle=0$, and show that the $z$-component $\langle s^z \rangle$ exhibits a domain-wall structure. We then study the entanglement properties of the chain. In particular, we derive upper and lower bounds for the von Neumann and Rényi entropies, and entanglement spectrum for any bipartition of the chain.

cond-mat.stat-mech↗

arXiv2017

Synergetic effect of spin-orbit coupling and Zeeman splitting on the optical conductivity in the one-dimensional Hubbard model

We study how the synergetic effect of spin-orbit coupling (SOC) and Zeeman splitting (ZS) affects the optical conductivity in the one-dimensional Hubbard model using the Kubo formula. We focus on two phenomena: (1) the electric dipole spin resonance (EDSR) in the metallic regime and (2) the optical conductivity in the Mott-insulating phase above the optical gap. In both cases, we calculate qualitatively the effects of SOC and ZS and how they depend on the relative angle between the SOC vector and the magnetic field direction. First, we investigate the spin resonance without electron correlation (the Hubbard parameter $U=0$). Although, neither SOC nor ZS causes any resonance by itself in the optical conductivity, the EDSR becomes possible when both of them exist. The resulting contribution to the optical conductivity is analyzed analytically. The effect of $U$ on the spin resonance is also studied with a numerical method. It is found that at half-filling, the resonance is first enhanced for small $U$ and then suppressed when the optical gap is large enough. In the strong coupling limit $U \rightarrow \infty$ at half-filling, we also refer to the resonance between the lower and upper Hubbard bands appearing at $ω\sim U$, above the optical gap. A large magnetic field tends to suppress the signal while it is recovered thanks to SOC depending on the relative angle of the magnetic field.

cond-mat.str-el↗

arXiv2017

Exact zero modes in twisted Kitaev chains

We study the Kitaev chain under generalized twisted boundary conditions, for which both the amplitudes and the phases of the boundary couplings can be tuned at will. We explicitly show the presence of exact zero modes for large chains belonging to the topological phase in the most general case, in spite of the absence of "edges" in the system. For specific values of the phase parameters, we rigorously obtain the condition for the presence of the exact zero modes in finite chains, and show that the zero modes obtained are indeed localized. The full spectrum of the twisted chains with zero chemical potential is analytically presented. Finally, we demonstrate the persistence of zero modes (level crossing) even in the presence of disorder or interactions.

cond-mat.mes-hall↗

arXiv2017

Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion

We introduce a lattice fermion model in one spatial dimension with supersymmetry (SUSY) but without particle number conservation. The Hamiltonian is defined as the anticommutator of two nilpotent supercharges $Q$ and $Q^\dagger$. Each supercharge is built solely from spinless fermion operators and depends on a parameter $g$. The system is strongly interacting for small $g$, and in the extreme limit $g=0$, the number of zero-energy ground states grows exponentially with the system size. By contrast, in the large-$g$ limit, the system is non-interacting and SUSY is broken spontaneously. We study the model for modest values of $g$ and show that under certain conditions spontaneous SUSY breaking occurs in both finite and infinite chains. We analyze the low-energy excitations both analytically and numerically. Our analysis suggests that the Nambu-Goldstone fermions accompanying the spontaneous SUSY breaking have cubic dispersion at low energies.

cond-mat.str-el↗

arXiv2017

Resonating Valence Bond States with Trimer Motifs

The trimer resonating valence bond (tRVB) state consisting of an equal-weight superposition of trimer coverings on a square lattice is proposed. A model Hamiltonian of the Rokhsar-Kivelson type for which the tRVB becomes the exact ground state is written. The state is shown to have $9^g$ topological degeneracy on genus g surface and support $Z_3$ vortex excitations. Correlation functions show exponential behavior with a very short correlation length consistent with the gapped spectrum. The classical problem of the degeneracy of trimer configurations is investigated by the transfer matrix method.

cond-mat.str-el↗

arXiv2016

Deformed Fredkin Spin Chain with Extensive Entanglement

We introduce a new spin chain which is a deformation of the Fredkin spin chain and has a phase transition between bounded and extensive entanglement entropy scaling. In this chain, spins have a local interaction of three nearest neighbors. The Hamiltonian is frustration-free and its ground state can be described analytically as a weighted superposition of Dyck paths. In the purely spin $1/2$ case, the entanglement entropy obeys an area law: it is bounded from above by a constant, when the size of the block $n$ increases (and $t>1$). When a local color degree of freedom is introduced the entanglement entropy increases linearly with the size of the block (and $t>1$). The entanglement entropy of half of the chain is tightly bounded by ${ n}\log s$ where $n$ is the size of the block, and $s$ is the number of colors. Our chain fosters a new example for a significant boost to entropy and for the existence of the associated critical rainbow phase where the entanglement entropy scales with volume that has recently been discovered in Zhang et al. (arXiv:1606.07795)

cond-mat.stat-mech↗

arXiv2016

Entanglement and corner Hamiltonian spectra of integrable open spin chains

Entanglement spectra (ES) for the critical SU(N) (2 <= N <= 4) spin chains and other integrable models of finite length are studied with the density matrix renormalization group method. For all models under investigation, the level spacings and the degeneracy structure of the ES are in excellent agreement with the spectra of the corner Hamiltonian, defined as the generator of the associated corner transfer matrix. The correspondence holds between the ES (n) at the n-th cut position from the edge of the spin model, and the corner Hamiltonian of length n, for all small values of n. The cut position dependence of the ES shows a period-N oscillatory behavior for a given SU(N) chain, reminiscent of the oscillatory part of the entanglement entropy observed in the past for the same models. Oscillations of the ES do not die out in the bulk of the chain, in contrast to the asymptotically vanishing oscillation of the entanglement entropy. Heuristic argument based on Young tableaux consideration can explain the period-N structure of the ES qualitatively.

cond-mat.str-el↗

arXiv2016

Supersymmetry breaking and Nambu-Goldstone fermions in an extended Nicolai model

We study a model of interacting spinless fermions in a one dimensional lattice with supersymmetry (SUSY). The Hamiltonian is given by the anti-commutator of two supercharges $Q$ and $Q^\dagger$, each of which is comprised solely of fermion operators and possesses one adjustable parameter $g$. When the parameter $g$ vanishes, the model is identical to the one studied by Nicolai [H. Nicolai, J. Phys. A: Math. Gen. \textbf{9}, 1497 (1976)], where the zero-energy ground state is exponentially degenerate. On the other hand, in the large-$g$ limit the model reduces to the free-fermion chain with a four-fold degenerate ground state. We show that for finite chains SUSY is spontaneously broken when $g > 0$. We also rigorously prove that for sufficiently large $g$ the ground-state energy density is nonvanishing in the infinite-volume limit. We further analyze the nature of the low-energy excitations by employing various techniques such as rigorous inequalities, exact numerical diagonalization, and renormalization group method with bosonization. The analysis reveals that the low-energy excitations are described by massless Dirac fermions (or Thirring fermions more generally), which can be thought of as Nambu-Goldstone fermions from the spontaneous SUSY breaking.

cond-mat.str-el↗

arXiv2016

Hofstadter's Butterfly in Quantum Geometry

We point out that the recent conjectural solution to the spectral problem for the Hamiltonian $H=e^{x}+e^{-x}+e^{p}+e^{-p}$ in terms of the refined topological invariants of a local Calabi-Yau geometry has an intimate relation with two-dimensional non-interacting electrons moving in a periodic potential under a uniform magnetic field. In particular, we find that the quantum A-period, determining the relation between the energy eigenvalue and the Kahler modulus of the Calabi-Yau, can be found explicitly when the quantum parameter $q=e^{i\hbar}$ is a root of unity, that its branch cuts are given by Hofstadter's butterfly, and that its imaginary part counts the number of states of the Hofstadter Hamiltonian. The modular double operation, exchanging $\hbar$ and $4π^2/\hbar$, plays an important role.

hep-th↗

arXiv2016

On the existence of an energy gap in one-dimensional Lesanovsky's model

We study the quantum lattice gas model in one dimension introduced by Lesanovsky, who showed that the exact ground state and a couple of excited states can be obtained analytically. The Hamiltonian of the model depends solely on the parameter $z$, the meaning of which is a fugacity in the corresponding classical lattice gas model. For small $z$ ($0<z<1$), we prove that there is an energy gap between the ground state and the excited states by applying Knabe's method.

cond-mat.quant-gas↗

arXiv2016

The $Z_2$ Index of Disordered Topological Insulators with Time Reversal Symmetry

We study disordered topological insulators with time reversal symmetry. Relying on the noncommutative index theorem which relates the Chern number to the projection onto the Fermi sea and the magnetic flux operator, we give a precise definition of the $Z_2$ index which is a noncommutative analogue of the Atiyah-Singer $Z_2$ index. We prove that the noncommutative $Z_2$ index is robust against any time-reversal symmetric perturbation including disorder potentials as long as the spectral gap at the Fermi level does not close.

math-ph↗

arXiv2015

Sine-square deformation and supersymmetric quantum mechanics

We investigate the sine-square deformation (SSD) of free fermions in one-dimensional continuous space. On the basis of supersymmetric quantum mechanics, we prove the correspondence between the many-body ground state of the system with SSD and that of the uniform system with periodic boundary conditions. We also discuss the connection between the SSD in the continuous space and its lattice version, where the geometric correction due to the real-space deformation plays an important role in relating the eigenstates of the lattice SSD with those of the continuous SSD.

cond-mat.stat-mech↗

arXiv2015

Exact ground states and topological order in interacting Kitaev/Majorana chains

We study a system of interacting spinless fermions in one dimension which, in the absence of interactions, reduces to the Kitaev chain [A. Yu Kitaev, Phys.-Usp. \textbf{44}, 131 (2001)]. In the non-interacting case, a signal of topological order appears as zero-energy modes localized near the edges. We show that the exact ground states can be obtained analytically even in the presence of nearest-neighbor repulsive interactions when the on-site (chemical) potential is tuned to a particular function of the other parameters. As with the non-interacting case, the obtained ground states are two-fold degenerate and differ in fermionic parity. We prove the uniqueness of the obtained ground states and show that they can be continuously deformed to the ground states of the non-interacting Kitaev chain without gap closing. We also demonstrate explicitly that there exists a set of operators each of which maps one of the ground states to the other with opposite fermionic parity. These operators can be thought of as an interacting generalization of Majorana edge zero modes.

cond-mat.str-el↗

arXiv2014

On integrable matrix product operators with bond dimension $D=4$

We construct and study a two-parameter family of matrix product operators of bond dimension $D=4$. The operators $M(x,y)$ act on $({\mathbb C}_2)^{\otimes N}$, i.e., the space of states of a spin-$1/2$ chain of length $N$. For the particular values of the parameters: $x=1/3$ and $y=1/\sqrt{3}$, the operator turns out to be proportional to the square root of the reduced density matrix of the valence-bond-solid state on a hexagonal ladder. We show that $M(x,y)$ has several interesting properties when $(x,y)$ lies on the unit circle centered at the origin: $x^2 + y^2=1$. In this case, we find that $M(x,y)$ commutes with the Hamiltonian and all the conserved charges of the isotropic spin-$1/2$ Heisenberg chain. Moreover, $M(x_1,y_1)$ and $M(x_2,y_2)$ are mutually commuting if $x^2_i + y^2_i=1$ for both $i=1$ and $2$. These remarkable properties of $M(x,y)$ are proved as a consequence of the Yang-Baxter equation.

cond-mat.stat-mech↗

arXiv2014

Composite-kink solutions of coupled nonlinear wave equations

We obtain exact traveling-wave solutions of the coupled nonlinear partial differential equations that describe the dynamics of two classical scalar fields in 1+1 dimensions. The solutions are kinks interpolating between neighboring vacua. We compute the classical kink mass and show that it saturates a Bogomol'nyi-type bound. We also present exact traveling-wave solutions of a more general class of models. Examples include coupled $ϕ^4$ and sine-Gordon models.

nlin.PS↗

arXiv2013

Phase diagram and pair Tomonaga-Luttinger liquid in a Bose-Hubbard model with flat bands

To explore superfluidity in flat-band systems, we consider a Bose-Hubbard model on a cross-linked ladder with $π$ flux, which has a flat band with a gap between the other band for noninteracting particles, where we study the effect of the on-site repulsion nonperturbatively. For low densities, we find exact degenerate ground states, each of which is a Wigner solid with nonoverlapping Wannier states on the flat band. At higher densities, the many-body system, when projected onto the lower flat band, can be mapped to a spin-chain model. This mapping enables us to reveal the existence of a Tomonaga-Luttinger liquid comprising it pairs of bosons. Interestingly, the high- and low- density regions have an overlap, where the two phases coexist.

cond-mat.str-el↗