arXiv subjects

D. N. Sheng

Publications and source records attributed to D. N. Sheng.

At least 127 records · Page 7Linked to original sources

arXiv2014

Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model

Kalmeyer-Laughlin (KL) chiral spin liquid (CSL) is a type of quantum spin liquid without time-reversal symmetry, and it is considered as the parent state of an exotic type of superconductivity--anyon superconductor. Such exotic state has been sought for more than twenty years, however it remains unclear whether it can exist in realistic system where time-reversal symmetry is breaking (T-breaking) spontaneously. By using the density matrix renormalization group, we show that KL CSL exists in a frustrated anisotropic kagome Heisenberg model (KHM), which has spontaneously T-breaking. We find that our model has two topological degenerate ground states, which exhibit non-vanishing scalar chirality order and are protected by finite excitation gap. Further, we identify this state as KL CSL by the characteristic edge conformal field theory from the entanglement spectrum and the quasiparticles braiding statistics extracted from the modular matrix. We also study how this CSL phase evolves as the system approaches the nearest neighbor KHM.

cond-mat.str-el↗

arXiv2014

Obtaining topological degenerate ground states by the density matrix renormalization group

We develop the density matrix renormalization group approach to systematically identify the topological order of the quantum spin liquid (QSL) through adiabatically obtaining different topological sectors of the QSL on an infinite cylinder. As an application, we study the anisotropic kagome Heisenberg model known for hosting a Z$_2$ QSL, however no numerical simulations have been able to access all four sectors before. We obtain the complete set of four topological degenerate ground states distinguished by the presence or absence of the spinon and vison quasiparticle line, which fully characterizes the topological nature of the quantum phase. We have also studied the kagome Heisenberg model, which has attracted a lot of recent attention. We find two topological sectors accurately and also estimate various properties of the other topological sectors, where the larger correlation length is found indicating the possible proximity to another phase.

cond-mat.str-el↗

arXiv2013

A Topological Spin Chern Pump

We propose a one-dimensional electron model with parameters modulated adiabatically in closed cycles, which can continuously pump spin to leads. By defining the spin-polarized Wannier functions, we show that the spin pump is protected by the spin Chern numbers, so that it is stable to perturbations violating the time-reversal symmetry and spin conservation. Our work demonstrates the possibility and principle to realize topological spin pumps independent of any symmetries, and also suggests a possible way to experimentally observe the bulk topological invariants.

cond-mat.mes-hall↗

arXiv2013

The scaling behavior of the insulator to plateau transition in topological band model

The scaling behavior of the quantum phase transition from an insulator to a quantum Hall plateau state has often been examined within systems realizing Landau levels. We study the topological transition in energy band models with nonzero Chern number, which have the same topological property as a Landau level. We find that the topological band generally realizes the same universality class as the integer quantum Hall system in magnetic field for strong enough disorder scattering. Furthermore, the symmetry of the transition characterized by the relations: $σ_{xy}(E)=1-σ_{xy}(-E)$ for the Hall conductance and $σ_{xx}(E)=σ_{xx}(-E)$ for the longitudinal conductance is observed near the transition region. We also establish that the finite temperature dependence of the Hall conductance is determined by the inelastic scattering relaxation time, while the localization exponent $ν$ remains unchanged by such scattering.

cond-mat.dis-nn↗

arXiv2013

Coupling-Matrix Approach to the Chern Number Calculation in Disordered Systems

The Chern number is often used to distinguish between different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline and disordered systems. To show its effectiveness, we apply the approach to the Haldane model and the lattice Hofstadter model, the quantized Chern numbers being correctly obtained. The disorder-induced topological phase transition is well reproduced, when the disorder strength is increased beyond the critical value. We expect the method to be widely applicable to the study of topological quantum numbers.

cond-mat.dis-nn↗

arXiv2013

Phase diagram of spin-1/2 J1-J2 Heisenberg model on honeycomb lattice

We use density matrix renormalization group (DMRG) algorithm to study the phase diagram of the spin-1/2 Heisenberg model on honeycomb lattice with first (J1) and second (J2) neighbor antiferromagnetic interactions, where a Z2 spin liquid region has been proposed. By implementing SU(2) symmetry in the DMRG code, we are able to obtain accurate results for long cylinders with width slightly over 15 lattice spacings and torus up to the size N=2*6*6. With increasing J2, we find a Neel phase with vanishing spin gap and a plaquette valence-bond (PVB) phase with non-zero spin gap. By extrapolating the square of the staggered magnetic moment ms^2 on finite-size cylinders to thermodynamic limit, we find the Neel order vanishing at J2/J1~0.22. For 0.25<J2/J1<0.35, we find a possible PVB order, which shows a fast growing PVB decay length with increasing system width. For 0.22<J2/J1<0.25, both spin and dimer orders are weak for all systems we have studied, which is consistent with a possible spin liquid phase or a deconfined quantum critical point. We present calculations of the topological entanglement entropy, compare the DMRG results with the variational Monte Carlo, and discuss possible scenarios in the thermodynamic limit for this region.

cond-mat.str-el↗

arXiv2013

Time-reversal symmetry breaking superconducting ground state in the doped Mott insulator on the honeycomb lattice

The emergence of superconductivity in doped Mott insulators has been debated for decades. In this paper, we report the theoretical discovery of a time-reversal symmetry breaking superconducting ground state in the doped Mott insulator (described by the well known t-J model) on honeycomb lattice, based on a recently developed variational method: the Grassmann tensor product state approach. As a benchmark, we use exact diagonalization and density-matrix renormalization methods to check our results on small clusters. We find systematic consistency for the ground-state energy as well as other physical quantities, such as the staggered magnetization. At low doping, the superconductivity coexists with antiferromagnetic ordering.

cond-mat.str-el↗

arXiv2013

Identifying Non-Abelian Topological Order through Minimal Entangled States

The topological order is equivalent to the pattern of long-range quantum entanglements, which cannot be measured by any local observable. Here we perform an exact diagonalization study to establish the non-Abelian topological order through entanglement entropy measurement. We focus on the quasiparticle statistics of the non-Abelian Moore-Read and Read-Rezayi states on the lattice boson models. We identify multiple independent minimal entangled states (MESs) in the groundstate manifold on a torus. The extracted modular $\mathcal{S}$ matrix from MESs faithfully demonstrates the Majorana quasiparticle or Fibonacci quasiparticle statistics, including the quasiparticle quantum dimensions and the fusion rules for such systems. These findings support that MESs manifest the eigenstates of quasiparticles for the non-Abelian topological states and encode the full information of the topological order.

cond-mat.str-el↗

arXiv2013

Emergent Space-time Supersymmetry at the Boundary of a Topological Phase

In contrast to ordinary symmetries, supersymmetry interchanges bosons and fermions. Originally proposed as a symmetry of our universe, it still awaits experimental verification. Here we theoretically show that supersymmetry emerges naturally in topological superconductors, which are well-known condensed matter systems. Specifically, we argue that the quantum phase transitions at the boundary of topological superconductors in both two and three dimensions display supersymmetry when probed at long distances and times. Supersymmetry entails several experimental consequences for these systems, such as, exact relations between quantities measured in disparate experiments, and in some cases, exact knowledge of the universal critical exponents. The topological surface states themselves may be interpreted as arising from spontaneously broken supersymmetry, indicating a deep relation between topological phases and SUSY. We discuss prospects for experimental realization in films of superfluid He$_3$-B.

cond-mat.str-el↗

arXiv2013

Stabilization of Quantum Spin Hall Effect by Designed Removal of Time-Reversal Symmetry of Edge States

The quantum spin Hall (QSH) effect is known to be unstable to perturbations violating time-reversal symmetry. We show that creating a narrow ferromagnetic (FM) region near the edge of a QSH sample can push one of the counterpropagating edge states to the inner boundary of the FM region, and leave the other at the outer boundary, without changing their spin polarizations and propagation directions. Since the two edge states are spatially separated into different "lanes", the QSH effect becomes robust against symmetry-breaking perturbations.

cond-mat.mes-hall↗

arXiv2013

Minimal Entangled States and Modular Matrix for Fractional Quantum Hall Effect in Topological Flat Bands

We perform an exact diagonalization study of the topological order in topological flat band models through calculating entanglement entropy and spectra of low energy states. We identify multiple independent minimal entangled states, which form a set of orthogonal basis states for the ground-state manifold. We extract the modular transformation matrices S (U) which contains the information of mutual (self) statistics, quantum dimensions and fusion rule of quasi-particles. Moreover, we demonstrate that these matrices are robust and universal in the whole topological phase against different perturbations until the quantum phase transition takes place.

cond-mat.str-el↗

arXiv2013

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau's Fermi-liquid theory is of central importance to many outstanding problems in condensed matter physics. One such problem is that, above the transition temperature and near optimal doping, high-transition-temperature copper-oxide superconductors exhibit `strange metal' behaviour that is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of a strange-metal quantum phase could shed new light on the interesting low-temperature behaviour in the pseudogap regime and on the d-wave superconductor itself. Here we present a theory for a specific example of a strange metal---the 'd-wave metal'. Using variational wavefunctions, gauge theoretic arguments, and ultimately large-scale density matrix renormalization group calculations, we show that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian---the usual t-J model with electron kinetic energy $t$ and two-spin exchange $J$ supplemented with a frustrated electron `ring-exchange' term, which we here examine extensively on the square lattice two-leg ladder. These findings constitute an explicit theoretical example of a genuine non-Fermi-liquid metal existing as the ground state of a realistic model.

cond-mat.str-el↗

arXiv2013

Topological phase transitions with and without energy gap closing

Topological phase transitions in a three-dimensional (3D) topological insulator (TI) with an exchange field of strength $g$ are studied by calculating spin Chern numbers $C^\pm(k_z)$ with momentum $k_z$ as a parameter. When $|g|$ exceeds a critical value $g_c$, a transition of the 3D TI into a Weyl semimetal occurs, where two Weyl points appear as critical points separating $k_z$ regions with different first Chern numbers. For $|g|<g_c$, $C^\pm(k_z)$ undergo a transition from $\pm 1$ to 0 with increasing $|k_z|$ to a critical value $k_z^{\tiny C}$. Correspondingly, surface states exist for $|k_z| < k_z^{\tiny C}$, and vanish for $|k_z| \ge k_z^{\tiny C}$. The transition at $|k_z| = k_z^{\tiny C}$ is acompanied by closing of spin spectrum gap rather than energy gap.

cond-mat.mes-hall↗

arXiv2012

Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two

Recent theoretical works have demonstrated various robust Abelian and non-Abelian fractional topological phases in lattice models with topological flat bands carrying Chern number C=1. Here we study hard-core bosons and interacting fermions in a three-band triangular-lattice model with the lowest topological flat band of Chern number C=2. We find convincing numerical evidence of bosonic fractional quantum Hall effect at the $ν=1/3$ filling characterized by three-fold quasi-degeneracy of ground states on a torus, a fractional Chern number for each ground state, a robust spectrum gap, and a gap in quasihole excitation spectrum. We also observe numerical evidence of a robust fermionic fractional quantum Hall effect for spinless fermions at the $ν=1/5$ filling with short-range interactions.

cond-mat.str-el↗

arXiv2012

Stacking-order dependence in thermoelectric transport of biased trilayer graphene

We numerically study the thermoelectric and thermal transport in trilayer graphene with different stacking orders in the presence of interlayer bias under a strong perpendicular magnetic field. In biased ABA-stacked case, we find that the thermoelectric conductivity displays different asymptotic behaviors with the varying of the temperature, similar to that of monolayer graphene. In the high temperature regime, the transverse thermoelectric conductivity $α_{xy}$ saturates to a universal value $2.77 k_B e/h$ at the center of each LL, while it displays a linear temperature dependence at low temperatures limit. The calculated transverse thermal conductivity $κ_{xy}$ exhibits two plateaus away from the band center. The transition between the two plateaus is continuous, which is accompanied by a pronounced peak in the longitudinal thermal conductivity $κ_{xx}$. In biased ABC-stacked case, it is found that both the thermoelectric conductivity and thermal conductivity have similar properties to the biased bilayer graphene, which is consistent with the behavior of a band insulator. The obtained results demonstrate the sensitivity of the thermoelectric conductivity to the band gap near the Dirac point. We also verify the validity of the Mott-relation and the generalized Wiedemann-Franz law.

cond-mat.mes-hall↗

arXiv2012

Fractional topological phases and broken time reversal symmetry in strained graphene

We show that strained or deformed honeycomb lattices are promising platforms to realize fractional topological quantum states in the absence of any magnetic field. The strained induced pseudo magnetic fields are oppositely oriented in the two valleys [1-3] and can be as large as 60-300 Tesla as reported in recent experiments [4,5]. For strained graphene at neutrality, a spin or a valley polarized state is predicted depending on the value of the onsite Coulomb interaction. At fractional filling, the unscreened Coulomb interaction leads to a valley polarized Fractional Quantum Hall liquid which spontaneously breaks time reversal symmetry. Motivated by artificial graphene systems [5-8], we consider tuning the short range part of interactions, and demonstrate that exotic valley symmetric states, including a valley Fractional Topological Insulator and a spin triplet superconductor, can be stabilized by such interaction engineering.

cond-mat.str-el↗

arXiv2012

Non-Abelian Quantum Hall Effect in Topological Flat Bands

Inspired by recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-Abelian quantum Hall effect (NA-QHE) in lattice models with topological flat bands (TFBs). Through extensive numerical studies on the Haldane model with three-body hard-core bosons loaded into a TFB, we find convincing numerical evidence of a stable $ν=1$ bosonic NA-QHE, with the characteristic three-fold quasi-degeneracy of ground states on a torus, a quantized Chern number, and a robust spectrum gap. Moreover, the spectrum for two-quasihole states also shows a finite energy gap, with the number of states in the lower energy sector satisfying the same counting rule as the Moore-Read Pfaffian state.

cond-mat.str-el↗

arXiv2012

Bose Metals and Insulators on Multi-Leg Ladders with Ring Exchange

We establish compelling evidence for the existence of new quasi-one-dimensional descendants of the d-wave Bose liquid (DBL), an exotic two-dimensional quantum phase of uncondensed itinerant bosons characterized by surfaces of gapless excitations in momentum space [O. I. Motrunich and M. P. A. Fisher, Phys. Rev. B {\bf 75}, 235116 (2007)]. In particular, motivated by a strong-coupling analysis of the gauge theory for the DBL, we study a model of hard-core bosons moving on the $N$-leg square ladder with frustrating four-site ring exchange. Here, we focus on four- and three-leg systems where we have identified two novel phases: a compressible gapless Bose metal on the four-leg ladder and an incompressible gapless Mott insulator on the three-leg ladder. The former is conducting along the ladder and has five gapless modes, one more than the number of legs. This represents a significant step forward in establishing the potential stability of the DBL in two dimensions. The latter, on the other hand, is a fundamentally quasi-one-dimensional phase that is insulating along the ladder but has two gapless modes and incommensurate power law transverse density-density correlations. In both cases, we can understand the nature of the phase using slave-particle-inspired variational wave functions consisting of a product of two distinct Slater determinants, the properties of which compare impressively well to a density matrix renormalization group solution of the model Hamiltonian. Stability arguments are made in favor of both quantum phases by accessing the universal low-energy physics with a bosonization analysis of the appropriate quasi-1D gauge theory. We will briefly discuss the potential relevance of these findings to high-temperature superconductors, cold atomic gases, and frustrated quantum magnets.

cond-mat.str-el↗