arXiv subjects

Erhai Zhao

Publications and source records attributed to Erhai Zhao.

At least 37 records · Page 2Linked to original sources

arXiv2020

Dynamical Singularities of Floquet Higher-Order Topological Insulators

We propose a versatile framework to dynamically generate Floquet higher-order topological insulators by multi-step driving of topologically trivial Hamiltonians. Two analytically solvable examples are used to illustrate this procedure to yield Floquet quadrupole and octupole insulators with zero- and/or $π$-corner modes protected by mirror symmetries. Furthermore, we introduce dynamical topological invariants from the full unitary return map and show its phase bands contain Weyl singularities whose topological charges form dynamical multipole moments in the Brillouin zone. Combining them with the topological index of Floquet Hamiltonian gives a pair of $\mathbb{Z}_2$ invariant $ν_0$ and $ν_π$ which fully characterize the higher-order topology and predict the appearance of zero- and $π$-corner modes. Our work establishes a systematic route to construct and characterize Floquet higher-order topological phases.

cond-mat.mes-hall↗

arXiv2019

Scrambling dynamics and many-body chaos in a random dipolar spin model

Is there a quantum many-body system that scrambles information as fast as a black hole? The Sachev-Ye-Kitaev model can saturate the conjectured bound for chaos, but it requires random all-to-all couplings of Majorana fermions that are hard to realize in experiments. Here we examine a quantum spin model of randomly oriented dipoles where the spin exchange is governed by dipole-dipole interactions. The model is inspired by recent experiments on dipolar spin systems of magnetic atoms, dipolar molecules, and nitrogen-vacancy centers. We map out the phase diagram of this model by computing the energy level statistics, spectral form factor, and out-of-time-order correlation (OTOC) functions. We find a broad regime of many-body chaos where the energy levels obey Wigner-Dyson statistics and the OTOC shows distinctive behaviors at different times: Its early-time dynamics is characterized by an exponential growth, while the approach to its saturated value at late times obeys a power law. The temperature scaling of the Lyapunov exponent $λ_L$ shows that while it is well below the conjectured bound $2πT$ at high temperatures, $λ_L$ approaches the bound at low temperatures and for large number of spins.

cond-mat.quant-gas↗

arXiv2019

Exactly Solvable Points and Symmetry-Protected Topological Phases of Quantum Spins on a Zig-Zag Lattice

A large number of symmetry-protected topological (SPT) phases have been hypothesized for strongly interacting spin-1/2 systems in one dimension. Realizing these SPT phases, however, often demands fine-tunings hard to reach experimentally. And the lack of analytical solutions hinders the understanding of their many-body wave functions. Here we show that two kinds of SPT phases naturally arise for ultracold polar molecules confined in a zigzag optical lattice. This system, motivated by recent experiments, is described by a spin model whose exchange couplings can be tuned by an external field to reach parameter regions not studied before for spin chains or ladders. Within the enlarged parameter space, we find the ground state wave function can be obtained exactly along a line and at a special point, for these two phases respectively. These exact solutions provide a clear physical picture for the SPT phases and their edge excitations. We further obtain the phase diagram by using infinite time-evolving block decimation, and discuss the phase transitions between the two SPT phases and their experimental signatures.

cond-mat.quant-gas↗

arXiv2018

Chiral to helical Majorana fermion transition in a $p$-wave superconductor

Chiral and helical Majorana edge modes are two archetypal gapless excitations of two-dimensional topological superconductors. They belong to superconductors from two different Altland-Zirnbauer symmetry classes characterized by $\mathbb{Z}$ and $\mathbb{Z}_2$ topological invariant respectively. It seems improbable to tune a pair of co-propagating chiral edge modes to counter-propagate without symmetry breaking. Here we show that such a direct topological transition is in fact possible, provided the system possesses an additional symmetry $\mathcal{O}$ which changes the bulk topological invariant to $\mathbb{Z}\oplus \mathbb{Z}$ type. A simple model describing the proximity structure of a Chern insulator and a $p_x$-wave superconductor is proposed and solved analytically to illustrate the transition between two topologically nontrivial phases. The weak pairing phase has two chiral Majorana edge modes, while the strong pairing phase is characterized by $\mathcal{O}$-graded Chern number and hosts a pair of counter-propagating Majorana fermions. The bulk topological invariants and edge theory are worked out in detail. Implications of these results to topological quantum computing based on Majorana fermions are discussed.

cond-mat.mes-hall↗

arXiv2018

Topological circuits of inductors and capacitors

Alternating current (ac) circuits can have electromagnetic edge modes protected by symmetries, analogous to topological band insulators or semimetals. How to make such a topological circuit? This paper illustrates a particular design idea by analyzing a series of topological circuits consisting purely of inductors (L) and capacitors (C) connected to each other by wires to form periodic lattices. All the examples are treated using a unifying approach based on Lagrangians and the dynamical $H$-matrix. First, the building blocks and permutation wiring are introduced using simple circuits in one dimension, the SSH transmission line and a braided ladder analogous to the ice-tray model also known as the $π$-flux ladder. Then, more general building blocks (loops and stars) and wiring schemes ($m$-shifts) are introduced. The key concepts of emergent pseudo-spin degrees of freedom and synthetic gauge fields are discussed, and the connection to quantum lattice Hamiltonians is clarified. A diagrammatic notation is introduced to simplify the design and presentation of more complicated circuits. These building blocks are then used to construct topological circuits in higher dimensions. The examples include the circuit analog of Haldane's Chern insulator in two dimensions and quantum Hall insulator in four dimensions featuring finite second Chern numbers. The topological invariants and symmetry protection of the edge modes are discussed based on the $H$-matrix.

cond-mat.mes-hall↗

arXiv2018

Weyl nodes in periodic structures of superconductors and spin active materials

Motivated by recent progress in epitaxial growth of proximity structures of s-wave superconductors (S) and spin-active materials (M), we show that the periodic structure of S and M can behave effectively as a superconductor with pairs of point nodes, near which the low energy excitations are Weyl fermions. A simple toy model, where M is described by a Kronig-Penney potential with both spin-orbit coupling and exchange field, is proposed and solved to obtain the phase diagram of the nodal structure, the spin texture of the Weyl fermions, as well as the zero energy surface states in the form of open Fermi lines ("Fermi arcs"). Going beyond the simple model, a lattice model with alternating layers of S and magnetic $Z_2$ topological insulators (M) is solved. The calculated spectrum confirms previous prediction of Weyl nodes based on tunneling Hamiltonian of Dirac electrons. Our results provide further evidence that periodic structures of S and M are well suited for engineering gapless topological superconductors.

cond-mat.supr-con↗

arXiv2018

Absence of long-range order in a triangular spin system with dipolar interactions

Antiferromagnetic Heisenberg model on the triangular lattice is perhaps the best known example of frustrated magnets, but it orders at low temperatures. Recent density matrix renormalization group (DMRG) calculations find that next nearest neighbor interaction $J_2$ enhances the frustration and leads to a spin liquid for $J_2/J_1\in (0.08,0.15)$. In addition, DMRG study of a dipolar Heisenberg model with longer range interactions gives evidence for a spin liquid at small dipole titling angle $θ\in[0,10^\circ)$. In both cases, the putative spin liquid region appears to be small. Here, we show that for the triangular lattice dipolar Heisenberg model, a robust quantum paramagnetic phase exists in a surprisingly wide region, $θ\in [0,54^\circ)$, for dipoles tilted along the lattice diagonal direction. We obtain the phase diagram of the model by functional renormalization group (RG) which treats all magnetic instabilities on equal footing. The quantum paramagnetic phase is characterized by a smooth continuous flow of vertex functions and spin susceptibility down to the lowest RG scale, in contrast to the apparent breakdown of RG flow in phases with stripe or spiral order. Our finding points to a promising direction to search for quantum spin liquids in ultracold dipolar molecules.

cond-mat.quant-gas↗

arXiv2018

Renormalization group analysis of dipolar Heisenberg model on square lattice

We present a detailed functional renormalization group analysis of spin-1/2 dipolar Heisenberg model on square lattice. This model is similar to the well known $J_1$-$J_2$ model and describes the pseudospin degrees of freedom of polar molecules confined in deep optical lattice with long-range anisotropic dipole-dipole interactions. Previous study of this model based on tensor network ansatz indicates a paramagnetic ground state for certain dipole tilting angles which can be tuned in experiments to control the exchange couplings. The tensor ansatz formulated on a small cluster unit cell is inadequate to describe the spiral order, and therefore the phase diagram at high azimuthal tilting angles remains undetermined. Here we obtain the full phase diagram of the model from numerical pseudofermion functional renormalization group calculations. We show that an extended quantum paramagnetic phase is realized between the Néel and stripe/spiral phase. In this region, the spin susceptibility flows smoothly down to the lowest numerical renormalization group scales with no sign of divergence or breakdown of the flow, in sharp contrast to the flow towards the long-range ordered phases. Our results provide further evidence that the dipolar Heisenberg model is a fertile ground for quantum spin liquids.

cond-mat.quant-gas↗

arXiv2017

Frustrated Magnetism of Dipolar Molecules on a Square Optical Lattice: Prediction of a Quantum Paramagnetic Ground State

Motivated by the experimental realization of quantum spin models of polar molecule KRb in optical lattices, we analyze the spin 1/2 dipolar Heisenberg model with competing anisotropic, long-range exchange interactions. We show that, by tilting the orientation of dipoles using an external electric field, the dipolar spin system on square lattice comes close to a maximally frustrated region similar, but not identical, to that of the $J_1$-$J_2$ model. This provides a simple yet powerful route to potentially realize a quantum spin liquid without the need for a triangular or kagome lattice. The ground state phase diagrams obtained from Schwinger-boson and spin-wave theories consistently show a spin disordered region between the N$\acute{\textrm{e}}$el, stripe, and spiral phase. The existence of a finite quantum paramagnetic region is further confirmed by an unbiased variational ansatz based on tensor network states and a tensor renormalization group.

cond-mat.quant-gas↗

arXiv2017

Theory of interacting fermions in shaken square optical lattice

We develop a theory of weakly interacting fermionic atoms in shaken optical lattices based on the orbital mixing in the presence of time-periodic modulations. Specifically, we focus on fermionic atoms in circularly shaken square lattice with near resonance frequencies, i.e., tuned close to the energy separation between $s$-band and the $p$-bands. First, we derive a time-independent four-band effective Hamiltonian in the non-interacting limit. Diagonalization of the effective Hamiltonian yields a quasi-energy spectrum consistent with the full numerical Floquet solution that includes all higher bands. In particular, we find that the hybridized $s$-band develops multiple minima and therefore non-trivial Fermi surfaces at different fillings. We then obtain the effective interactions for atoms in the hybridized $s$-band analytically and show that they acquire momentum dependence on the Fermi surface even though the bare interaction is contact-like. We apply the theory to find the phase diagram of fermions with weak attractive interactions and demonstrate that the pairing symmetry is $s+d$-wave. Our theory is valid for a range of shaking frequencies near resonance, and it can be generalized to other phases of interacting fermions in shaken lattices.

cond-mat.quant-gas↗

arXiv2016

Competing many-body instabilities in two-dimensional dipolar Fermi gases

Experiments on quantum degenerate Fermi gases of magnetic atoms and dipolar molecules begin to probe their broken symmetry phases dominated by the long-range, anisotropic dipole-dipole interaction. Several candidate phases including the p-wave superfluid, the stripe density wave, and a supersolid have been proposed theoretically for two-dimensional spinless dipolar Fermi gases. Yet the phase boundaries predicted by different approximations vary greatly, and a definitive phase diagram is still lacking. Here we present a theory that treats all competing many-body instabilities in the particle-particle and particle-hole channel on equal footing. We obtain the low temperature phase diagram by numerically solving the functional renormalization-group flow equations and find a nontrivial density wave phase at small dipolar tilting angles and strong interactions, but no evidence of the supersolid phase. We also estimate the critical temperatures of the ordered phases.

cond-mat.quant-gas↗

arXiv2016

Anatomy of a periodically driven p-wave superconductor

The topological properties of periodically driven many-body systems often have no static analogs and defy a simple description based on the effective Hamiltonian. To explore the emergent edge modes in driven p-wave superconductors in two dimensions, we analyze a toy model of Kitaev chains (one-dimensional spinless p-wave superconductors with Majorana edge states) coupled by time-periodic hopping. We show that with proper driving, the coupled Kitaev chains can turn into a fully gapped superconductor which is analogous to the $p_x+ip_y$ state but has two, rather than one, chiral edge modes. A different driving protocol turns it into a gapless superconductor with isolated point nodes and completely flat edge states at quasienergy $ω=0$ or $π/T$, with $T$ the driving period. The time evolution operator $U(k_x,k_y,t)$ of the toy model is computed exactly to yield the phase bands. And the "topological singularities" of the phase bands are exhausted and compared to those of a periodically driven Hofstadter model which features counter-propagating chiral edge modes. These examples demonstrate the unique edge states in driven superconducting systems and suggest driving as a potentially fruitful route to engineer new topological superconductors.

cond-mat.supr-con↗

arXiv2016

Cosine Edge Mode in a Periodically Driven Quantum System

Time-periodic (Floquet) topological phases of matter exhibit bulk-edge relationships that are more complex than static topological insulators and superconductors. Finding the edge modes unique to driven systems usually requires numerics. Here we present a minimal two-band model of Floquet topological insulators and semimetals in two dimensions where all the bulk and edge properties can be obtained analytically. It is based on the extended Harper model of quantum Hall effect at flux one half. We show that periodical driving gives rise to a series of phases characterized by a pair of integers. The model has a most striking feature: the spectrum of the edge modes is always given by a single cosine function, $ω(k_y)\propto \cos k_y$ where $k_y$ is the wave number along the edge, as if it is freely dispersing and completely decoupled from the bulk. The cosine mode is robust against the change in driving parameters and persists even to semi-metallic phases with Dirac points. The localization length of the cosine mode is found to contain an integer and in this sense quantized.

cond-mat.quant-gas↗

arXiv2016

A continuum of compass spin models on the honeycomb lattice

Quantum spin models with spatially dependent interactions, known as compass models, play an important role in the study of frustrated quantum magnetism. One example is the Kitaev model on the honeycomb lattice with spin-liquid ground states and anyonic excitations. Another example is the geometrically frustrated quantum $120^\circ$ model on the same lattice whose ground state has not been unambiguously established. To generalize the Kitaev model beyond the exactly solvable limit and connect it with other compass models, we propose a new model, dubbed "the tripod model", which contains a continuum of compass-type models. It smoothly interpolates the Ising model, the Kitaev model, and the quantum $120^\circ$ model by tuning a single parameter $θ'$, the angle between the three legs of a tripod in the spin space. Hence it not only unifies three paradigmatic spin models, but also enables the study of their quantum phase transitions. We obtain the phase diagram of the tripod model numerically by tensor networks in the thermodynamic limit. We show that the ground state of the quantum $120^\circ$ model has long-range dimer order. Moreover, we find an extended spin-disordered (spin-liquid) phase between the dimer phase and an antiferromagnetic phase. The unification and solution of a continuum of frustrated spin models as outline here may be useful to exploring new domains of other quantum spin or orbital models.

cond-mat.quant-gas↗

arXiv2014

Spin-orbital exchange of strongly interacting fermions on the $p$-band of a two-dimensional optical lattice

Mott insulators with both spin and orbital degeneracy are pertinent to a large number of transition metal oxides. The intertwined spin and orbital fluctuations can lead to rather exotic phases such as quantum spin-orbital liquids. Here we consider two-component (spin 1/2) fermionic atoms with strong repulsive interactions on the $p$-band of the optical square lattice. We derive the spin-orbital exchange for quarter filling of the $p$-band when the density fluctuations are suppressed, and show it frustrates the development of long range spin order. Exact diagonalization indicates a spin-disordered ground state with ferro-orbital order. The system dynamically decouples into individual Heisenberg spin chains, each realizing a Luttinger liquid accessible at higher temperatures compared to atoms confined to the $s$-band.

cond-mat.quant-gas↗

arXiv2014

Floquet edge states in a harmonically driven integer quantum Hall system

Recent theoretical work on time-periodically kicked Hofstadter model found robust counter-propagating edge modes. It remains unclear how ubiquitously such anomalous modes can appear, and what dictates their robustness against disorder. Here we shed further light on the nature of these modes by analyzing a simple type of periodic driving where the hopping along one spatial direction is modulated sinusoidally with time while the hopping along the other spatial direction is kept constant. We obtain the phase diagram for the quasienergy spectrum at flux 1/3 as the driving frequency $ω$ and the hopping anisotropy are varied. A series of topologically distinct phases with counter-propagating edge modes appear due to the harmonic driving, similar to the case of a periodically kicked system studied earlier. We analyze the time dependence of the pair of Floquet edge states localized at the same edge, and compare their Fourier components in the frequency domain. In the limit of small modulation, one of the Floquet edge mode within the pair can be viewed as the edge mode originally living in the other energy gap shifted in quasienergy by $\hbar ω$, i.e., by absorption or emission of a "photon" of frequency $ω$. Our result suggests that counter-propagating Floquet edge modes are generic features of periodically driven integer quantum Hall systems, and not tied to any particular driving protocol. It also suggests that the Floquet edge modes would remain robust to any static perturbations that do not destroy the chiral edge modes of static quantum Hall states.

cond-mat.quant-gas↗

arXiv2014

Counter-propagating edge modes and topological phases of a kicked quantum Hall system

A periodically driven quantum Hall system in a fixed magnetic field is found to exhibit a series of phases featuring anomalous edge modes with the "wrong" chirality. This leads to pairs of counter-propagating chiral edge modes at each edge, in sharp contrast to stationary quantum Hall systems. We show that the pair of Floquet edge modes are protected by the chiral (sublattice) symmetry, and that they are robust against static disorder. The existence of distinctive phases with the same Chern and winding numbers but very different edge state spectra points to the important role played by symmetry in classifying topological properties of driven systems. We further explore the evolution of the edge states with driving using a simplified model, and discuss their experimental signatures.

cond-mat.quant-gas↗

arXiv2013

Quantum phases of quadrupolar Fermi gases in optical lattices

We introduce a new platform for quantum simulation of many-body systems based on nonspherical atoms or molecules with zero dipole moment but possessing a significant value of electric quadrupole moment. We consider a quadrupolar Fermi gas trapped in a 2D square optical lattice, and show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interaction results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and opens up a perspective to create topological superfluid. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities.

cond-mat.quant-gas↗