arXiv subjects

Shinsei Ryu

Publications and source records attributed to Shinsei Ryu.

At least 145 records · Page 8Linked to original sources

arXiv2016

Determination of Tomonaga-Luttinger parameters for a two-component liquid

We provide evidence for the mapping of critical spin-1 chains, in particular the SU(3) symmetric bilinear-biquadratic model with additional interactions, to free boson theories using exact diagonalization and the density matrix renormalization group algorithm. Using the correspondence with a conformal field theory with central charge c=2, we determine the analytic formulae for the scaling dimensions in terms of four Tomonaga-Luttinger liquid parameters. By matching the lowest scaling dimensions, we numerically calculate these field-theoretic parameters and track their evolution as a function of the parameters of the lattice model.

cond-mat.str-el↗

arXiv2015

Viscoelastic response of topological tight-binding models in two and three dimensions

The topological response to external perturbations is an effective probe to characterize different topological phases of matter. Besides the Hall conductance, the Hall viscosity is another example of such a response that measures how electronic wave functions respond to changes in the underlying geometry. Topological (Chern) insulators are known to have a quantized Hall conductance. A natural question is how the Hall viscosity behaves for these materials. So far, most of studies on the Hall viscosity of Chern insulators have focused on the continuum limit. The presence of lattice breaks the continuous translational symmetry to a discrete group and this causes two complications: it introduces a new length scale associated with the lattice constant, and makes the momentum periodic. We develop two different methods of how to implement a lattice deformation: (1) a lattice distortion is encoded as a shift in the lattice momentum, and (2) a lattice deformation is treated microscopically in the gradient expansion of the hopping matrix elements. After establishing the method of deformation we can compute the Hall viscosity through a linear response (Kubo) formula. We examine these methods for three models: the Hofstadter model, the Chern insulator, and the surface of a 3D topological insulator. Our results in certain regimes of parameters, where the continuum limit is relevant, are in agreement with previous calculations. We also provide possible experimental signatures of the Hall viscosity by studying the phononic properties of a single crystal 3D topological insulator.

cond-mat.mes-hall↗

arXiv2015

Effective hydrodynamic field theory and condensation picture of topological insulators

While many features of topological band insulators are commonly discussed at the level of single-particle electron wave functions, such as the gapless Dirac spectrum at their boundary, it remains elusive to develop a {\it hydrodynamic} or {\it collective} description of fermionic topological band insulators in 3+1 dimensions. As the Chern-Simons theory for the 2+1-dimensional quantum Hall effect, such a hydrodynamic effective field theory provides a universal description of topological band insulators, even in the presence of interactions, and that of putative fractional topological insulators. In this paper, we undertake this task by using the functional bosonization. The effective field theory in the functional bosonization is written in terms of a two-form gauge field, which couples to a $U(1)$ gauge field that arises by gauging the continuous symmetry of the target system (the $U(1)$ particle number conservation). Integrating over the $U(1)$ gauge field by using the electromagnetic duality, the resulting theory describes topological band insulators as a condensation phase of the $U(1)$ gauge theory (or as a monopole condensation phase of the dual gauge field). The hydrodynamic description, and the implication of its duality, of the surface of topological insulators are also discussed. We also touch upon the hydrodynamic theory of fractional topological insulators by using the parton construction.

cond-mat.str-el↗

arXiv2015

Entanglement negativity after a local quantum quench in conformal field theories

We study the time evolution of the entanglement negativity after a local quantum quench in (1+1)-dimensional conformal field theories (CFTs), which we introduce by suddenly joining two initially decoupled CFTs at their endpoints. We calculate the negativity evolution for both adjacent intervals and disjoint intervals explicitly. For two adjacent intervals, the entanglement negativity grows logarithmically in time right after the quench. After developing a plateau-like feature, the entanglement negativity drops to the ground-state value. For the case of two spatially separated intervals, a light-cone behavior is observed in the negativity evolution; in addition, a long-range entanglement, which is independent of the distance between two intervals, can be created. Our results agree with the heuristic picture that quasiparticles, which carry entanglement, are emitted from the joining point and propagate freely through the system. Our analytical results are confirmed by numerical calculations based on a critical harmonic chain.

cond-mat.stat-mech↗

arXiv2015

Topological Phases Protected By Reflection Symmetry and Cross-cap States

Twisting symmetries provides an efficient method to diagnose symmetry-protected topological (SPT) phases. In this paper, edge theories of (2+1)-dimensional topological phases protected by reflection as well as other symmetries are studied by twisting reflection symmetry, which effectively puts the edge theories on an unoriented spacetime, such as the Klein bottle. A key technical step taken in this paper is the use of the so-called cross-cap states, which encode entirely the unoriented nature of spacetime, and can be obtained by rearranging the spacetime geometry and exchanging the role of space and time coordinates. When the system is in a non-trivial SPT phase, we find that the corresponding cross-cap state is non-invariant under the action of the symmetries of the SPT phase, but acquires an anomalous phase. This anomalous phase, with a proper definition of a reference state, on which symmetry acts trivially, reproduces the known classification of (2+1)-dimensional bosonic and fermionic SPT phases protected by reflection symmetry, including in particular the Z_8 classification of topological crystalline superconductors protected by reflection and time-reversal symmetries.

cond-mat.str-el↗

arXiv2015

Effective response theory for zero energy Majorana bound states in three spatial dimensions

We propose a gravitational response theory for point defects (hedgehogs) binding Majorana zero modes in (3+1)-dimensional superconductors. Starting in 4+1 dimensions, where the point defect is extended into a line, a coupling of the bulk defect texture with the gravitational field is introduced. Diffeomorphism invariance then leads to an $SU(2)_2$ Kac-Moody current running along the defect line. The $SU(2)_2$ Kac-Moody algebra accounts for the non-Abelian nature of the zero modes in 3+1 dimensions. It is then shown to also encode the angular momentum density which permeates throughout the bulk between hedgehog-anti-hedgehog pairs.

cond-mat.other↗

arXiv2015

Topological BF theory of the quantum hydrodynamics of incompressible polar fluids

We analyze a hydrodynamical model of a polar fluid in (3+1)-dimensional spacetime. We explore a spacetime symmetry -- volume preserving diffeomorphisms -- to construct an effective description of this fluid in terms of a topological BF theory. The two degrees of freedom of the BF theory are associated to the mass (charge) flows of the fluid and its polarization vorticities. We discuss the quantization of this hydrodynamic theory, which generically allows for fractionalized excitations. We propose an extension of the Girvin-MacDonald-Platzman algebra to (3+1)-dimensional spacetime by the inclusion of the vortex-density operator in addition to the usual charge density operator and show that the same algebra is obeyed by massive Dirac fermions that represent the bulk of $\mathbb{Z}^{\,}_{2}$ topological insulators in three-dimensional space.

cond-mat.mes-hall↗

arXiv2014

Boundary States as Holographic Duals of Trivial Spacetimes

We study real-space quantum entanglement included in conformally invariant boundary states in conformal field theories (CFTs). First, we argue that boundary states essentially have no real-space entanglement by computing the entanglement entropy when we bipartite the system into two spatial regions. From the viewpoint of holography, this shows that boundary states are dual to trivial spacetimes of zero spactime volume. Next, we point out that a continuous multiscale entanglement renormalization ansatz (cMERA) for any CFTs can be formulated by employing a boundary state as its infrared unentangled state with an appropriate regularization. Exploiting this idea, we propose an approximation scheme of cMERA construction for general CFTs.

hep-th↗

arXiv2014

Majorana vortex-bound states in three-dimensional nodal noncentrosymmetric superconductors

Noncentrosymmetric superconductors (NCSs), characterized by antisymmetric spin-orbit coupling and a mixture of spin-singlet and spin-triplet pairing components, are promising candidate materials for topological superconductivity. An important hallmark of topological superconductors is the existence of protected zero-energy states at surfaces or in vortex cores. Here we investigate Majorana vortex-bound states in three-dimensional nodal and fully gapped NCSs by combining analytical solutions of Bogoliubov-de Gennes (BdG) equations in the continuum with exact diagonalization of BdG Hamiltonians. We show that depending on the crystal point-group symmetries and the topological properties of the bulk Bogoliubov-quasiparticle wave functions, different types of zero-energy Majorana modes can appear inside the vortex core. We find that for nodal NCSs with tetragonal point group $C_{4v}$ the vortex states are dispersionless along the vortex line, forming one-dimensional Majorana flat bands, while for NCSs with $D_{4}$ point-group symmetry the vortex modes are helical Majorana states with a linear dispersion along the vortex line. NCSs with monoclinic point group $C_2$, on the other hand, do not exhibit any zero-energy vortex-bound states. We show that in the case of the $C_{4v}$ ($D_4$) point group the stability of these Majorana zero modes is guaranteed by a combination of reflection ($π$ rotation), time-reversal, and particle-hole symmetry. Considering continuous deformations of the quasiparticle spectrum in the presence of vortices, we show that the flat-band vortex-bound states of $C_{4v}$ point-group NCSs can be adiabatically connected to the dispersionless vortex-bound states of time-reversal symmetric Weyl superconductors. Experimental implications of our results for thermal transport and tunneling measurements are discussed.

cond-mat.supr-con↗

arXiv2014

Symmetry-protected entangling boundary zero modes in crystalline topological insulators

Crystalline topological insulators owe their topological character to the protection that certain boundary states acquire because of certain point-group symmetries. We first show that a Hermitian operator obeying supersymmetric quantum mechanisms (SUSY QM) delivers the entanglement spectrum. We then show that such an entanglement spectrum that is compatible with a certain point-group symmetry obeys a certain local spectral symmetry. The latter result is applied to the stability analysis of four fermionic non-interacting Hamiltonians, the last of which describes graphene with a Kekule distortion. All examples have the remarkable property that their entanglement spectra inherit a local spectral symmetry from either an inversion or reflection symmetry that guarantees the stability of gapless boundary entangling states, even though all examples fail to support protected gapless boundary states at their physical boundaries.

cond-mat.str-el↗

arXiv2014

CPT theorem and classification of topological insulators and superconductors

We present a systematic topological classification of fermionic and bosonic topological phases protected by time-reversal, particle-hole, parity, and combination of these symmetries. We use two complementary approaches: one in terms of K-theory classification of gapped quadratic fermion theories with symmetries, and the other in terms of the K-matrix theory description of the edge theory of (2+1)-dimensional bulk theories. The first approach is specific to free fermion theories in general spatial dimensions while the second approach is limited to two spatial dimensions but incorporates effects of interactions. We also clarify the role of CPT theorem in classification of symmetry-protected topological phases, and show, in particular, topological superconductors dis- cussed before are related by CPT theorem.

cond-mat.str-el↗

arXiv2014

Conflicting Symmetries in Topologically Ordered Surface States of Three-dimensional Bosonic Symmetry Protected Topological Phases

We study the Z2 topologically ordered surface state of three-dimensional bosonic SPT phases with the discrete symmetries G1 x G2. It has been argued that the topologically ordered surface state cannot be realized on a purely two-dimensional lattice model. We carefully examine the statement and show that the surface state should break G2 if the symmetry G1 is gauged. This manifests the conflict of the symmetry G1 and G2 on the surface of the three-dimensional SPT phase. Given that there is no such phenomena in the purely two-dimensional model, it signals that the symmetries are encoded anomalously on the surface of the three-dimensional SPT phases and that the surface state can never be realized on the purely two-dimensional models.

cond-mat.str-el↗

arXiv2014

Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds

We generalize Laughlin's flux insertion argument, originally discussed in the context of the quantum Hall effect, to topological phases protected by non-on-site unitary symmetries, in particular by parity symmetry or parity symmetry combined with an on-site unitary symmetry. As a model, we discuss fermionic or bosonic systems in two spatial dimensions with CP symmetry, which are, by the CPT theorem, related to time-reversal symmetric topological insulators (e.g., the quantum spin Hall effect). In particular, we develop the stability/instability (or "gappability"/"ingappablity") criteria for non-chiral conformal field theories with parity symmetry that may emerge as an edge state of a symmetry-protected topological phase. A necessary ingredient, as it turns out, is to consider the edge conformal field theories on unoriented surfaces, such as the Klein bottle, which arises naturally from enforcing parity symmetry by a projection operation.

cond-mat.str-el↗

arXiv2014

Spin-directed network model for the surface states of weak three-dimensional $\mathbb{Z}^{\,}_{2}$ topological insulators

A two-dimensional spin-directed $\mathbb{Z}^{\,}_{2}$ network model is constructed that describes the combined effects of dimerization and disorder for the surface states of a weak three-dimensional $\mathbb{Z}^{\,}_{2}$ topological insulator. The network model consists of helical edge states of two-dimensional layers of $\mathbb{Z}^{\,}_{2}$ topological insulators which are coupled by time-reversal symmetric interlayer tunneling. It is argued that, without dimerization of interlayer couplings, the network model has no insulating phase for any disorder strength. However, a sufficiently strong dimerization induces a transition from a metallic phase to an insulating phase. The critical exponent $ν$ for the diverging localization length at metal-insulator transition points is obtained by finite-size scaling analysis of numerical data from simulations of this network model. It is shown that the phase transition belongs to the two-dimensional symplectic universality class of Anderson transition.

cond-mat.mes-hall↗

arXiv2014

Interaction effect on topological classification of superconductors in two dimensions

We introduce a new class of superconductors (SCs) in two spatial dimensions with time reversal symmetry and reflection (i.e., mirror) symmetry. In the absence of interactions, topological classes of these SCs are distinguished by an integer-valued ($\mathbb{Z}$) topological invariant. When interactions are included, we show that the topological classification is modified to $\mathbb{Z}_8$. This clearly demonstrates that interactions can have qualitative effect on topological classifications of gapped states of matter in more than one dimension.

cond-mat.str-el↗

arXiv2013

Holographic Geometry of cMERA for Quantum Quenches and Finite Temperature

We study the time evolution of cMERA (continuous MERA) under quantum quenches in free field theories. We calculate the corresponding holographic metric using the proposal of arXiv:1208.3469 and confirm that it qualitatively agrees with its gravity dual given by a half of the AdS black hole spacetime, argued by Hartman and Maldacena in arXiv:1303.1080. By doubling the cMERA for the quantum quench, we give an explicit construction of finite temperature cMERA. We also study cMERA in the presence of chemical potential and show that there is an enhancement of metric in the infrared region corresponding to the Fermi energy.

hep-th↗

arXiv2013

Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument

We consider non-chiral symmetry-protected topological phases of matter in two spatial dimensions protected by a discrete symmetry such as $\mathbb{Z}_K$ or $\mathbb Z_K \times \mathbb Z_K $ symmetry. We argue that modular invariance/noninvariance of the partition function of the one-dimensional edge theory can be used to diagnose whether, by adding a suitable potential, the edge theory can be gapped or not without breaking the symmetry. By taking bosonic phases described by Chern-Simons K-matrix theories and fermionic phases relevant to topological superconductors as an example, we demonstrate explicitly that when the modular invariance is achieved, we can construct an interaction potential that is consistent with the symmetry and can completely gap out the edge.

cond-mat.str-el↗

arXiv2013

Diffusive transport in Weyl semimetals

Diffusion, a ubiquitous phenomenon in nature, is a consequence of particle number conservation and locality, in systems with sufficient damping. In this paper we consider diffusive processes in the bulk of Weyl semimetals, which are exotic quantum materials, recently of considerable interest. In order to do this, we first explicitly implement the analytical scheme by which disorder with anisotropic scattering amplitude is incorporated into the diagrammatic response-function formalism for calculating the `diffuson'. The result thus obtained is consistent with transport coefficients evaluated from the Boltzmann transport equation or the renormalized uniform current vertex calculation, as it should be. We thus demonstrate that the computation of the diffusion coefficient should involve the transport lifetime, and not the quasiparticle lifetime. Using this method, we then calculate the density response function in Weyl semimetals and discover an unconventional diffusion process that is significantly slower than conventional diffusion. This gives rise to relaxation processes that exhibit stretched exponential decay, instead of the usual exponential diffusive relaxation. This result is then explained using a model of thermally excited quasiparticles diffusing with diffusion coefficients which are strongly dependent on their energies. We elucidate the roles of the various energy and time scales involved in this novel process and propose an experiment by which this process may be observed.

cond-mat.mes-hall↗