arXiv subjects

Hsin-Hua Lai

Publications and source records attributed to Hsin-Hua Lai.

35 records · Page 2Linked to original sources

arXiv2015

Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems

We demonstrate that the entanglement entropy area law for free fermion ground states and the corresponding volume law for highly excited states are related by a position-momentum duality, thus of the same origin. For a typical excited state in the thermodynamic limit, we further show that the reduced density matrix of a subsystem approaches thermal density matrix, provided the subsystem's linear size is small compared to that of the whole system in all directions, a property we dub eigenstate typicality. This provides an explicit example of thermalization via entanglement, and reveals how statistical physics emerges from a single eigenstate by tracing out a large number of degrees of freedom.

cond-mat.stat-mech↗

arXiv2015

Short-ranged interaction effects on $Z_2$ topological phase transitions: The perturbative mean-field method

Time-reversal symmetric topological insulator is a novel state of matter that a bulk-insulating state carries dissipationless spin transport along the surfaces, embedded by the $Z_2$ topological invariant. In the noninteracting limit, this exotic state has been intensively studied and explored with realistic systems, such as HgTe/(Hg,Cd)Te quantum wells. Yet an interacting topological insulator is still an elusive subject, and most related analyses rely on the mean-field approximation and numerical simulations. Among the approaches, the mean-field approximation fails to predict the topological phase transition, in particular at intermediate interaction strength without spontaneously breaking symmetry. In this review, we develop an analytical approach based on a combined perturbative and self-consistent mean-field treatment of interactions that is capable of capturing topological phase transitions beyond either method when used independently. As an illustration of the method, we study the effects of short-ranged interactions on the $Z_2$ topological insulator phase, also known as the quantum spin Hall phase, in three generalized versions of the Kane-Mele model at half-filling on the honeycomb lattice. The results are in excellent agreement with quantum Monte Carlo calculations on the same model, and cannot be reproduced by either a perturbative treatment or a self-consistent mean-field treatment of the interactions. Our analytical approach helps to clarify how the symmetries of the one-body terms of the Hamiltonian determine whether interactions tend to stabilize or destabilize a topological phase. Moreover, our method should be applicable to a wide class of models where topological transitions due to interactions are in principle possible, but are not correctly predicted by either perturbative or self-consistent treatments.

cond-mat.str-el↗

arXiv2014

Disordered and interacting parabolic semimetals in two and three dimensions

A clean noninteracting parabolic semimetal is characterized by quadratic band touching between the conduction and the valence bands at isolated diabolic points in the Brillouin zone and describes a fermionic quantum critical system with dynamic exponent z=2. We consider the stability of such a semimetal against electronic interaction and quenched disorder using a perturbative renormalization group analysis for two and three spatial dimensions. For the noninteracting problem infinitesimally weak disorder leads to an Anderson insulator and a diffusive metal respectively in two and three dimensions. On the other hand, the long range Coulomb interaction causes an excitonic instability for the clean interacting problem towards a broken symmetry ground state in both dimensions. Our weak coupling analysis of the combined effects of disorder and interaction suggests the competition between a broken symmetry and a disorder controlled metallic or insulating states, but is inadequate for describing the quantum phase transitions among them. We discuss the relevance of our results for bilayer graphene and some 227 iridate compounds, and identify these materials as promising candidates for exploring novel disorder and interaction controlled quantum critical phenomena.

cond-mat.str-el↗

arXiv2014

Effects of short-ranged interactions on the Kane-Mele model without discrete particle-hole symmetry

We study the effects of short-ranged interactions on the $Z_2$ topological insulator phase, also known as the quantum spin Hall phase, in the Kane-Mele model at half-filling with staggered potentials which explicitly breaks the discrete particle-hole symmetry. Within Hartree-Fock mean-field analysis, we conclude that the on-site repulsive interactions help stabilize the topological phase (quantum spin Hall) against the staggered potentials by enlarging the regime of the topological phase along the axis of the ratio of the staggered potential strength and the spin-orbit coupling. In sharp contrast, the on-site attractive interactions destabilize the topological phase. We also examine the attractive interaction case by means of the unbiased determinant projector quantum Monte Carlo and the results are qualitatively consistent with the Hartree-Fock picture.

cond-mat.str-el↗

arXiv2014

Short-ranged interaction effects on $Z_2$ topological phase transitions

Using a combined perturbative and self-consistent mean-field approach that we directly compare with quantum Monte Carlo calculations, we study the effects of short-ranged interactions on the $Z_2$ topological insulator phase, also known as the quantum spin Hall phase, in two generalized versions of the Kane-Mele model at half-filling on the honeycomb lattice. For interactions weaker than the critical value for magnetic instability, we find that the interactions can stabilize the quantum spin Hall phase against third neighbor hoppings, which preserve $C_3$ lattice rotation symmetry, but destabilize it for a dimerization that explicitly breaks the $C_3$ symmetry. Consistent with quantum Monte Carlo calculations, we show the phase boundary shifts are linearly proportional to the square of the interaction strength, but with opposite sign--a result that cannot be reproduced with a perturbative treatment that does not also include a self-consistent treatment of the perturbed Hamiltonian. Our results emphasize that short-range interactions can have subtle effects on the stability of topological phases, and may need to be treated by methods analogous to those we use here.

cond-mat.str-el↗

arXiv2013

Violation of Entanglement-Area Law in Bosonic Systems with Bose Surfaces: Possible Application to Bose Metals

We show the violation of the entanglement-area law for bosonic systems with Bose surfaces. For bosonic systems with gapless factorized energy dispersions on a N^d Cartesian lattice in d-dimension, e.g., the exciton Bose liquid in two dimension, we explicitly show that a belt subsystem with width L preserving translational symmetry along d-1 Cartesian axes has leading entanglement entropy (N^{d-1}/3)ln L. Using this result, the strong subadditivity inequality, and lattice symmetries, we bound the entanglement entropy of a rectangular subsystem from below and above showing a logarithmic violation of the area law. For subsystems with a single flat boundary we also bound the entanglement entropy from below showing a logarithmic violation, and argue that the entanglement entropy of subsystems with arbitrary smooth boundaries are similarly bounded.

quant-ph↗

arXiv2013

Possible spin liquid states with parton Fermi surfaces in SU(3) ring-exchange model on the triangular lattice

We consider a SU(3) ring-exchange model on a triangular lattice. Unlike the SU(2) case, under perturbation expansion of the SU(3) Hubbard model, the three-site ring exchange is present as well as the usual four-site ring exchange. Interestingly, the three-site ring exchange differs from the usual two-site and four-site exchanges by a minus sign and is ferromagnetic. We first present numerical site-factorized state studies on this model which shows a three-sublatticed order phase and a ferromagnetic phase. We further study the model using slave-fermion mean field in which we rewrite the exchange operators in terms of three flavors of fermions. We find the main competing trial states are the trimer state (triangular plaquette state) and the gapless U(1) spin liquid states with parton Fermi surfaces which include both the uniform zero-flux spin liquid state, and the uniform π-flux spin liquid state. Furthermore, we find there are possible pairing instabilities of the zero-flux (Fermi surface) spin liquid state toward a f-wave gapless (nodal) spin liquid state and the π-flux (Fermi surface) spin liquid state toward an interesting exotic s-wave ``gapless`` spin liquid state with two flavors of fermions paired up while one flavor of fermions remains gapless.

cond-mat.str-el↗

arXiv2013

Possible uniform-flux chiral spin liquid states in the SU(3) ring-exchange model on the triangular lattice

We consider a SU(3) model with antiferromagnetic three-site ring exchanges, in addition to two-site exchanges, on the triangular lattice. We first present numerical site-factorized state studies on the magnetic ordered states, which shows two different three-sublattice-ordered states, the antiferro-quadrupolar phase and the standard 120^o anti-ferromagnetic phase, along the axis of the strength of the three-site ring exchanges. We further study the model using slave-fermion mean field approaches in which we rewrite the exchange operators in terms of three flavors of fermions. At the mean-field level, we find the main competing trial states are the trimer state (triangular plaquette state), gapped uniform π/3-flux chiral spin liquid, and gapped uniform 2π/3-flux chiral spin liquid. The filled band of the π/3-flux chiral spin liquid has Chern number +1, and that of the 2π/3-flux chiral spin liquid has Chern number +2. We also give the effective Chern-Simons theory for each chiral spin liquid at the mean-field level.

cond-mat.str-el↗

arXiv2013

Distinguishing particle-hole conjugated Fractional Quantum Hall states using quantum dot mediated edge transport

We study theoretically edge transport of a fractional quantum Hall liquid, in the presence of a quantum dot inside the Hall bar with well controlled electron density and Landau level filling factor ν, and show that such transport studies can help reveal the nature of the fractional quantum Hall liquid. In our first example we study the ν=1/3 and ν=2/3 liquids in the presence of a ν=1 quantum dot. When the quantum dot becomes large, its edge states join those of the Hall bar to reconstruct the edge states configuration. Taking randomness around the edges into account, we find that in the disorder-irrelevant phase the two-terminal conductance of the original ν=1/3 system vanishes at zero temperature, while that of the ν=2/3 case remains finite. This distinction is rooted in the fact that the ν=2/3 state is built upon the ν=1 state. In the disorder-dominated phase, the two-terminal conductance of ν=1/3 system is (1/5)\frac{e^2}{h} and that of ν=2/3 system is (1/2)\frac{e^2}{h}. We further apply the same idea to the ν=5/2 system which realizes either the Pfaffian or the anti-Pfaffian states. In this case we study the edge transport in the presence of a central ν=3 quantum dot. If the quantum dot is large enough for its edge states joining those of the Hall bar, in the disorder-irrelevant phase the total two-terminal conductance in the Pfaffian case is G^{Pf}_{tot}\rightarrow 2 \frac{e^2}{h} while that of anti-Pfaffian case is higher but not universal, G^{aPf}_{tot}> 2 \frac{e^2}{h}. This difference can be used to determine which one of these two states is realized at ν=5/2. In the disorder-dominated phase, however, the total two-terminal conductances in these two systems are exactly the same, G^{Pf/aPf}_{tot}=(7/3)\frac{e^2}{h}.

cond-mat.str-el↗

arXiv2012

Majorana Spin Liquids on a two-leg ladder

We realize a gapless Majorana Orbital Liquid (MOL) using orbital degrees of freedom and also an SU(2)-invariant Majorana Spin Liquid (MSL) using both spin and orbital degrees of freedom in Kitaev-type models on a 2-leg ladder. The models are exactly solvable by Kitaev's parton approach, and we obtain long-wavelength descriptions for both Majorana liquids. The MOL has one gapless mode and power law correlations in energy at incommensuare wavevectors, while the SU(2) MSL has three gapless modes and power law correlations in spin, spin-nematic, and local energy observables. We study the stability of such states to perturbations away from the exactly solvable points. We find that both MOL and MSL can be stable against allowed short-range parton interactions. We also argue that both states persist upon allowing $Z_2$ gauge field fluctuations, in that the number of gapless modes is retained, although with an expanded set of contributions to observables compared to the free parton mean field.

cond-mat.str-el↗

arXiv2011

SU(2)-invariant Majorana spin liquid with stable parton Fermi surfaces in an exactly solvable model

We construct an exactly solvable spin-orbital model on a decorated square lattice that realizes an SU(2)-invariant Majorana spin liquid with parton Fermi surfaces, of the kind discussed recently by Biswas et al. [ Phys. Rev. B. {\bf 83}, 245131(2011)]. We find power-law spin correlations as well as power-law spin-nematic correlations with the same dominant $1/|{\bf r}|^3$ envelope. The model is solvable also in the presence of Zeeman magnetic field. One fermion species carries $S^z=0$ quantum number and its Fermi surface is not altered in the field, while the Fermi surfaces of the other species evolve and can disappear. In particular, we find an interesting half-magnetization plateau phase in which spin excitations are gapful while there remain spinless gapless excitations that still produce metal-like thermal properties. In the fully-magnetized phase, the model reduces to the one proposed by Baskaran et al., [arXiv:0908.1614v3] in terms of the orbital degrees of freedom.

cond-mat.str-el↗

arXiv2011

Power-Law Behavior of Bond Energy Correlators in a Kitaev-type Model with a Stable Parton Fermi Surface

We study bond energy correlation functions in an exactly solvable quantum spin model of Kitaev type on the kagome lattice with stable Fermi surface of partons proposed recently by Chua et al, Ref.\[arXiv:1010.1035]. Even though any spin correlations are ultra-short ranged, we find that the bond energy correlations have power law behavior with a $1/|{\bm r}|^3$ envelope and oscillations at incommensurate wavevectors. We determine the corresponding singular surfaces in momentum space, which provide a gauge-invariant characterization of this gapless spin liquid.

cond-mat.str-el↗

arXiv2010

Insulating phases of electrons on a zigzag strip in the orbital magnetic field

We consider electrons on a two-leg triangular ladder at half-filling and in an orbital magnetic field. In a two-band regime in the absence of the field, the electronic system remains conducting for weak interactions since there is no four-fermion Umklapp term. We find that in the presence of the orbital field there is a four-fermion Umklapp and it is always relevant for repulsive interactions. Thus in this special ladder, the combination of the orbital magnetic field and interactions provides a mechanism to drive metal-insulator transition already at weak coupling. We discuss properties of the possible resulting phases C0S2 and various C0S1 and C0S0.

cond-mat.str-el↗

arXiv2010

Effects of impurities in Spin Bose-Metal phase on a two-leg triangular strip

We study effects of nonmagnetic impurities in a Spin Bose-Metal (SBM) phase discovered in a two-leg triangular strip spin-1/2 model with ring exchanges (D. N. Shenget al, arXiv:0902.4210). This phase is a quasi-1D descendant of a 2D spin liquid with spinon Fermi sea, and the present study aims at interpolating between the 1D and 2D cases. Different types of defects can be treated as local energy perturbations, which we find are always relevant. As a result, a nonmagnetic impurity generically cuts the system into two decoupled parts. We calculate bond energy and local spin susceptibility near the defect, both of which can be measured in experiments. The Spin Bose-Metal has dominant correlations at characteristic incommensurate wavevectors that are revealed near the defect. Thus, the bond energy shows a static texture oscillating as a function of distance from the defect and decaying as a slow power law. The local spin susceptibility also oscillates and actually {\it increases} as a function of distance from the defect, similar to the effect found in the 1D chain [S. Eggert and I. Affleck, Phys. Rev. Lett. {\bf 75}, 934 (1995)]. We calculate the corresponding power law exponents for the textures as a function of one Luttinger parameter of the SBM theory.

cond-mat.str-el↗

arXiv2010

Effects of Zeeman field on a Spin Bose-Metal phase

We consider Zeeman field effects on a Spin Bose-Metal (SBM) phase on a two-leg triangular ladder. This phase was found in a spin-1/2 model with ring exchanges [D. N. Sheng et. al., Phys. Rev. B {\bf 79}, 205112 (2009)], and was also proposed to appear in an interacting electronic model with longer-ranged repulsion [Lai et. al., Phys. Rev. B {\bf 81}, 045105 (2010)]. Using bosonization of a spinon-gauge theory, we study the stability of the SBM phase and its properties under the field. We also explore phases arising from potential instabilities of the SBM; in all cases, we find a gap to spin-1 excitations while spin-nematic correlations are power law. We discuss two-dimensional analogues of these phases where spinons can pair with their own species.

cond-mat.str-el↗

arXiv2009

Two-band electronic metal and neighboring spin liquid (spin Bose-metal) on a zigzag strip with longer-ranged repulsion

We consider an electronic model for realizing the Spin Bose-metal (SBM) phase on a 2-leg triangular strip --a spin liquid phase found by D. N. Sheng et al [Phys. Rev. B {\bf 79}, 205112 (2009)] in a spin-1/2 model with ring exchanges. The SBM can be viewed as a "C1S2" Mott insulator of electrons where the overall charge transporting mode is gapped out. We start from a two-band "C2S2" metal and consider extended repulsion motivated by recent ab initio derivation of electronic model for $κ$-ET spin liquid material [K. Nakamura et al, J. Phys. Soc. Jpn. {\bf 78}, 083710(2009)]. Using weak coupling renormalization group analysis, we find that the extended interactions allow much wider C2S2 metallic phase than in the Hubbard model with on-site repulsion only. An eight-fermion Umklapp term plays a crucial role in producing a Mott insulator but can not be treated in weak coupling. We use Bosonization to extend the analysis to intermediate coupling and study phases obtained out of the C2S2 metal upon increasing overall repulsion strength, finding that the SBM phase is a natural outcome for extended interactions.

cond-mat.str-el↗

arXiv2009

Spatial trends of non-collinear exchange coupling mediated by itinerant carriers with different Fermi surfaces

We study the exchange coupling mediated by itinerant carriers with spin-orbit interaction by both analytic and numeric approaches. The mediated exchange coupling is non-collinear and its spatial trends depend on the Fermi surface topology of the itinerant carriers. Taking Rashba interaction as an example, the exchange coupling is similar to the conventional Ruderman-Kittel-Kasuya-Yosida type in weak coupling. On the other hand, in the strong coupling, the spiral interaction dominates. In addition, inclusion of finite spin relaxation always makes the non-collinear spiral exchange interaction dominant. Potential applications of our findings are explained and discussed.

cond-mat.mes-hall↗