arXiv subjects

Ying-Hai Wu

Publications and source records attributed to Ying-Hai Wu.

At least 37 records · Page 2Linked to original sources

arXiv2023

Continuous phase transitions between fractional quantum Hall states and symmetry-protected topological states

We study quantum phase transitions in Bose-Fermi mixtures driven by interspecies interaction in the quantum Hall regime. In the absence of such an interaction, the bosons and fermions form their respective fractional quantum Hall (FQH) states at certain filling factors. A symmetry-protected topological (SPT) state is identified as the ground state for strong interspecies interaction. The phase transitions between them are proposed to be described by Chern-Simons-Higgs field theories. For a simple microscopic Hamiltonian, we present numerical evidence for the existence of the SPT state and a continuous transition to the FQH state. It is also found that the entanglement entropy between the bosons and fermions exhibits scaling behavior in the vicinity of this transition.

cond-mat.str-el↗

arXiv2023

Generalized Calogero-Sutherland models for Kondo physics in the Luttinger liquid

We propose a series of models with inverse-square interactions, for which the ground states have an exact closed form, that describe one localized spin-$1/2$ Kondo impurity coupled to Luttinger liquids of itinerant bosons or fermions in the continuum or on a lattice. The model Hamiltonians contain two parts: a two-component Calogero-Sutherland model with open boundary condition in the continuum or a long-range $t \textendash J$-type model on the lattice, and long-range Kondo couplings between the impurity and the particles. The wave functions of the ground states in a certain basis have Jastrow product forms with powers depending on the particle statistics. It is shown that the wave functions can be expressed as chiral correlators of certain conformal field theories, which reveals that the particles are fractionalized to fully screen the Kondo impurity. This insight would be very useful in future studies on the very difficult problem of Kondo physics with interacting baths.

cond-mat.str-el↗

arXiv2022

Two-component parton fractional quantum Hall state in graphene

We study the $ν={\pm}1/2$ fractional quantum Hall states in graphene observed by Zibrov et al. [Nat. Phys. 14, 930 (2018)]. The parton construction is employed to provide a valley unpolarized trial wave function for these states. The lattice scale valley anisotropic terms in the Hamiltonian soften the repulsion between electrons in different valleys to favor the valley unpolarized state. The validity of our proposal is corroborated by numerical calculations.

cond-mat.str-el↗

arXiv2022

Topological states in double monolayer graphene

Motivated by the experiments on double monolayer graphene that observe a variety of fractional quantum Hall states [Liu et al., Nat. Phys. 15, 893 (2019); Li et al., Nat. Phys. 15, 898 (2019)], we study the special setting in which two monolayers have different areas. It has not been considered before and allows us to construct a class of exotic topological states. The elementary excitations of these states do not carry fractional charges but obey fractional statistics. This is in sharp contrast to all previously studied cases, where the two properties are intimately connected and serve as hallmarks of fractional quantum Hall states. Numerical calculations are performed to demonstrate that some states can be realized with realistic parameters.

cond-mat.str-el↗

arXiv2022

Non-Abelian topological order with SO(5)$_{1}$ chiral edge states

We consider a chiral spin liquid constructed using the parton theory. This state supports non-Abelian anyons and neutral fermions, which share some similarities with the celebrated Moore-Read state. The edge physics of the parton state and the Moore-Read state is very different. Based on conformal field theory (CFT) analysis, it is proposed that the edge states exhibit an emergent SO(5) symmetry. The counting of edge states in the low-lying SO(5)$_{1}$ CFT towers is computed. The chiral spin liquid is generated using tensor network methods, which allows us to confirm the SO(5)$_{1}$ counting using entanglement spectrum. An additional feature of multiple branches in the entanglement spectrum is observed and analyzed.

cond-mat.str-el↗

arXiv2022

Chiral conformal field theory for topological states and the anyon eigenbasis on the torus

Model wave functions constructed from (1+1)D conformal field theory (CFT) have played a vital role in studying chiral topologically ordered systems. There usually exist multiple degenerate ground states when such states are placed on the torus. The common practice for dealing with this degeneracy within the CFT framework is to take a full correlator on the torus, which includes both holomorphic and antiholomorphic sectors, and decompose it into several conformal blocks. In this paper, we propose a pure chiral approach for the torus wave function construction. By utilizing the operator formalism, the wave functions are written as chiral correlators of holormorphic fields restricted to each individual topological sector. This method is not only conceptually much simpler, but also automatically provides us the anyon eigenbasis of the degenerate ground states (also known as the "minimally entangled states"). As concrete examples, we construct the full set of degenerate ground states for SO($n$)$_1$ and SU($n$)$_1$ chiral spin liquids on the torus, the former of which provide a complete wave function realization of Kitaev's sixteenfold way of anyon theories. We further characterize their topological orders by analytically computing the associated modular $S$ and $T$ matrices.

cond-mat.str-el↗

arXiv2021

Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus

We propose resonating valence bond wave functions for a spin-1 system on the torus that realize a non-Abelian chiral spin liquid. The wave functions take the form of infinite dimensional matrix product states constructed from conformal blocks of the $\mathrm{SO}(3)_{1}$ Wess-Zumino-Witten model. This means that they are lattice analogues of the bosonic Moore-Read state introduced in fractional quantum Hall systems. The topological order of this system is revealed by explicit construction of three-fold degenerate ground states and analytical computation of the modular S and T matrices.

cond-mat.str-el↗

arXiv2020

Quantum phases of two-component bosons on the Harper-Hofstadter ladder

We study two-component bosons on the Harper-Hofstadter model with two legs. The synthetic magnetic fields for the two types of bosons point to either the same direction or opposite directions. The bosons have hardcore intra-species interaction such that there can be no more than one boson of the same type on each lattice site. For certain filling factors in the absence of inter-species interaction, each component realizes a vortex Mott insulator with rung current or a Meissner superfluid without rung current. The system undergoes phase transitions to other phases as inter-species interaction is turned on, which are characterized numerically using the density matrix renormalization group method and supplemented with analytical studies when possible. The vortex Mott insulator transits to a gapped Meissner phase without rung current and the Meissner superfluid transits to a gapped vortex phase with rung current. In both cases, we observe gapped spin density wave states that break certain ${\mathbb Z}_{2}$ symmetries.

cond-mat.quant-gas↗

arXiv2020

Tensor network representations of parton wave functions

Tensor network states and parton wave functions are two pivotal methods for studying quantum many-body systems. This work connects these two subjects as we demonstrate that a variety of parton wave functions, such as projected Fermi sea and projected fermionic or bosonic paired states, can be represented exactly as tensor networks. The results can be compressed into matrix product states with moderate bond dimensions so various physical quantities can be computed efficiently. For the projected Fermi sea, we develop an excellent compression scheme with high fidelity using maximally localized Wannier orbitals. Numerical calculations on two parton wave functions demonstrate that our method exceeds commonly adopted Monte Carlo methods in some aspects. It produces energy and correlation function with very high accuracy that is difficult to achieve using Monte Carlo method. The entanglement measures that were almost impossible to compute before can also be obtained easily using our method.

cond-mat.str-el↗

arXiv2019

Effective Abelian theory from a non-Abelian topological order in $ν=2/5$ fractional quantum Hall effect

Topological phases of matter are distinguished by topological invariants, such as Chern numbers and topological spins, that quantize their response to electromagnetic currents and changes of ambient geometry. Intriguingly, in the $ν=2/5$ fractional quantum Hall effect, prominent theoretical approaches -- the composite fermion theory and conformal field theory -- have constructed two distinct states, the Jain composite fermion (CF) state and the Gaffnian state, for which many of the topological indices coincide and even the microscopic ground state wave functions have high overlap with each other in system sizes accessible to numerics. At the same time, some aspects of these states are expected to be very different, e.g., their elementary excitations should have either Abelian (CF) or non-Abelian (Gaffnian) statistics. In this paper we investigate the close relationship between these two states by considering not only their ground states, but also the low-energy charged excitations. We show that the low-energy physics of both phases is spanned by the same type of quasielectrons of the neighbouring Laughlin phase. The main difference between the two states arises due to an implicit assumption of short-range interaction in the CF approach, which causes a large splitting of the variational energies of the Gaffnian excitations. We thus propose that the Jain phase emerges as an effective Abelian low-energy description of the Gaffnian phase when the Hamiltonian is dominated by two-body interactions of sufficiently short range.

cond-mat.str-el↗

arXiv2019

Quantum impurity models from conformal field theory

The coupling between localized magnetic moments and itinerant electrons presents a plethora of interesting physics. The low-energy physics of some quantum impurity systems can be described using conformal field theory (CFT). In this paper, the connection between quantum impurity models and CFT is further strengthened as we construct a class of exactly solvable models with ground states given by CFT correlators. The method developed here is completely analytical and can be applied to fermions with an arbitrary number of colors and multiple impurities. Numerical calculations are performed to characterize certain aspects of our models for which we do not have analytical results.

hep-th↗

arXiv2019

Exactly solvable quantum impurity model with inverse-square interactions

We construct an exactly solvable quantum impurity model which consists of spin-1/2 conduction fermions and the spin-1/2 magnetic moment. The ground state is a Gutzwiller projected Fermi sea with non-orthonormal modes and its wave function in the site-occupation basis is a Jastrow-type homogeneous polynomial. The parent Hamiltonian has all-to-all inverse-square hopping terms between the conduction fermions and inverse-square spin-exchange terms between the conduction fermions and the magnetic moments. The low-lying energy levels, spin-spin correlation function, and von Neumann entanglement entropy of our model demonstrate that it exhibits the essential aspects of spin-1/2 Kondo physics. The machinery developed in this work can generate many other exactly solvable quantum impurity models.

cond-mat.str-el↗

arXiv2019

Chiral topological states in Bose-Fermi mixtures

Topological states were initially discovered in solid state systems and have generated widespread interest in many areas of physics. The advances in cold atoms create novel settings for studying topological states that would be quite unrealistic in solid state systems. One example is that the constituents of quantum gases can be various types of bosons, fermions, and their mixtures. This paper explores interaction-induced topological states in two-dimensional Bose-Fermi mixture. We propose a class of topological states which have no fractionalized excitations but possess maximally chiral edge states. For previously known topological states, these two features can only be found simultaneously in the integer quantum Hall states of fermions and the $E_{8}$ state of bosons. The existences of some proposed states in certain continuum and lattice models are corroborated by exact diagonalization and density matrix renormalization group calculations. This paper suggests that Bose-Fermi mixture is a very appealing platform for studying topological states.

cond-mat.str-el↗

arXiv2018

Possible SU(3) Chiral Spin Liquid on the Kagome Lattice

We propose an SU(3) symmetric Hamiltonian with short-range interactions on the Kagome lattice and show that it hosts an Abelian chiral spin liquid (CSL) state. We provide numerical evidence based on exact diagonalization to show that this CSL state is stabilized in an extended region of the parameter space and can be viewed as a lattice version of the Halperin 221 fractional quantum Hall (FQH) state of two-component bosons. We also construct a parton wave function for this CSL state and demonstrate that its variational energies are in good agreement with exact diagonalization results. The parton description further supports that the CSL is characterized by a chiral edge conformal field theory (CFT) of the SU(3)_1 Wess-Zumino-Witten type.

cond-mat.str-el↗

arXiv2018

Superconducting spin properties of Majorana nanowires and the associated superconducting anomalous Hall effect

It is difficult to unambiguously confirm the existence of Majorana zero modes (MZMs) due to the absence of smoking-gun signatures in charge transport measurements. Recent studies suggest that the spin degree of freedom of MZMs may provide an alternative detection method. We study the spin properties of the superconducting state in Majorana nanowires and the associated unconventional Josephson effect with realistic experimental parameters taken from [Zhang {\it et al.}, Nature 556, 74 (2018)]. For a superconducting thin film with in-plane polarized spin-triplet pairing, an out-of-plane electric field can generate a supercurrent perpendicular to both the superconducting spin polarization and the electric field, so we name this phenomena as superconducting anomalous Hall effect (ScAHE). In a Majorana nanowire, the regime with finite polarized spin-triplet pairing almost coincides with the chiral regime, which includes the topological regime. We further study the effects of polarized spin-triplet pairing in two types of Josephson junctions. One dramatic finding is that SOC can induce an anomalous supercurrent at zero phase difference only in the U-shape junction, a basic ingredient of scalable topological quantum computation. This can be viewed as a consequence of the ScAHE. Our work reveals that the spin degree of freedom is indeed helpful for detecting MZMs.

cond-mat.mes-hall↗

arXiv2018

Non-Abelian Chiral Spin Liquid on the Kagome Lattice

We study $S=1$ spin liquid states on the kagome lattice constructed by Gutzwiller-projected $p_x+ip_y$ superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices $S$ and $T$, we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the $SO(3)_1$ (or, equivalently, $SU(2)_2$) field theory predictions. We propose a local Hamiltonian which may stabilize the NACSL. From a variational study we observe a topological phase transition from the NACSL to the $Z_2$ Abelian spin liquid.

cond-mat.str-el↗

arXiv2017

Chiral Spin Condensation in a One-Dimensional Optical Lattice

We study a spinor (two-component) Bose gas confined in a one-dimensional double-valley optical lattice which has a double-well structure in momentum space. Based on field theory analysis, it is found that spinor bosons in the double-valley band may form a spin-charge mixed chiral spin quasicondensate under certain conditions. Our numerical calculations in a concrete $π$-flux triangular ladder system confirm the robustness of the chiral spin order against interactions and quantum fluctuations. This exotic atomic Bose-Einstein condensate exhibits spatially staggered spin loop currents without any charge dynamics despite the complete absence of spin-orbit coupling in the system, creating an interesting approach to atom spintronics. The entanglement entropy scaling allows us to extract conformal-field-theory central charge and establish the low-energy effective field theory for the chiral spin condensate as a two-component Luttinger liquid. Our predictions should be detectable in atomic experiments through spin-resolved time-of-flight techniques.

cond-mat.quant-gas↗

arXiv2017

Composite Fermions on a Torus

We achieve an explicit construction of the lowest Landau level (LLL) projected wave functions for composite fermions in the periodic (torus) geometry. To this end, we first demonstrate how the vortex attachment of the composite fermion (CF) theory can be accomplished in the torus geometry to produce the "unprojected" wave functions satisfying the correct (quasi-)periodic boundary conditions. We then consider two methods for projecting these wave functions into the LLL. The direct projection produces valid wave functions but can be implemented only for very small systems. The more powerful and more useful projection method of Jain and Kamilla fails in the torus geometry because it does not preserve the periodic boundary conditions and thus takes us out of the original Hilbert space. We have succeeded in constructing a modified projection method that is consistent with both the periodic boundary conditions and the general structure of the CF theory. This method is valid for a large class of states of composite fermions, called "proper states," which includes the incompressible ground states at electron filling factors $ν=\frac{n}{2pn+ 1}$, their charged and neutral excitations, and also the quasidegenerate ground states at arbitrary filling factors of the form $ν=\frac{ν^*}{2pν^*+ 1}$, where $n$ and $p$ are integers and $ν^*$ is the CF filling factor. Comparison with exact results known for small systems for the ground and excited states at filling factors $ν=1/3$, 2/5 and 3/7 demonstrates our LLL-projected wave functions to be extremely accurate representations of the actual Coulomb eigenstates. Our construction enables the study of large systems of composite fermions on the torus, thereby opening the possibility of investigating numerous interesting questions and phenomena.

cond-mat.str-el↗