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Yue Yu

Publications and source records attributed to Yue Yu.

At least 487 records · Page 27Linked to original sources
arXiv2011

Abelian and non-abelian anyons in integer quantum anomalous Hall effect and topological phase transitions via superconducting proximity effect

We study the quantum anomalous Hall effect described by a class of two-component Haldane models on square lattices. We show that the latter can be transformed into a pseudospin triplet p+ip-wave paired superfluid. In the long wave length limit, the ground state wave function is described by Halperin's (1,1,-1) state of neutral fermions analogous to the double layer quantum Hall effect. The vortex excitations are charge e/2 abelian anyons which carry a neutral Dirac fermion zero mode. The superconducting proximity effect induces `tunneling' between `layers' which leads to topological phase transitions whereby the Dirac fermion zero mode fractionalizes and Majorana fermions emerge in the edge states. The charge e/2 vortex excitation carrying a Majorana zero mode is a non-abelian anyon. The proximity effect can also drive a conventional insulator into a quantum anomalous Hall effect state with a Majorana edge mode and the non-abelian vortex excitations.

cond-mat.str-el↗
arXiv2011

Three-body interactions on a triangular lattice

We analyze the hard-core Bose-Hubbard model with both the three-body and nearest neighbor repulsions on the triangular lattice. The phase diagram is achieved by means of the semi-classical approximation and the quantum Monte Carlo simulation. For a system with only the three-body interactions, both the supersolid phase and one third solid disappear while the two thirds solid stably exists. As the thermal behavior of the bosons with nearest neighbor repulsion, the solid and the superfluid undergo the 3-state Potts and the Kosterlitz-Thouless type phase transitions, respectively. In a system with both the frustrated nearest neighbor two-body and three-body interactions, the supersolid and one third solid revive. By tuning the strength of the three-body interactions, the phase diagram is distorted, because the one-third solid and the supersolid are suppressed.

cond-mat.quant-gas↗
arXiv2010

Correlation-hole induced paired quantum Hall states in lowest Landau level

A theory is developed for the paired even-denominator fractional quantum Hall states in the lowest Landau level. We show that electrons bind to quantized vortices to form composite fermions, interacting through an exact instantaneous interaction that favors chiral p-wave pairing. Two canonically dual pairing gap functions are related by the bosonic Laughlin wavefunction (Jastraw factor) due to the correlation holes. We find that the ground state is the Moore-Read pfaffian in the long wavelength limit for weak Coulomb interactions, a new pfaffian of an oscillatory pairing function for intermediate interactions, and a Read-Rezayi composite Fermi liquid beyond a critical interaction strength. Our findings are consistent with recent experimental observations of the 1/2 and 1/4 fractional quantum Hall effects in asymmetric wide quantum wells.

cond-mat.str-el↗
arXiv2010

Simulating Wess-Zumino Supersymmetry Model in Optical Lattices

We study a cold atom-molecule mixture in two-dimensional optical lattices, in which fermionic atoms have a Dirac-type dispersion. We show that by fine-tuning the atomic and molecular interactions, such mixtures can simulate Wess-Zumino supersymmetry (SUSY) model, the first example of SUSY theories. At zero temperature, SUSY is not spontaneously broken for this simplest SUSY model, which implies identical relativistic dispersions of the atom and its superpartner, bosonic diatom molecule. This defining signature of SUSY can be probed by single particle spectroscopies. Thermal breaking of SUSY at finite temperature is accompanied by a thermal Goldstone fermion, i.e., phonino excitation. This and other signatures of broken SUSY can also be probed experimentally.

cond-mat.quant-gas↗
arXiv2010

An anyon model in a toric honeycomb lattice

We study an anyon model in a toric honeycomb lattice. The ground states and the low-lying excitations coincide with those of Kitaev toric code model and then the excitations obey mutual semionic statistics. This model is helpful to understand the toric code of anyons in a more symmetric way. On the other hand, there is a direct relation between this toric honeycomb model and a boundary coupled Ising chain array in a square lattice via Jordan-Wigner transformation. We discuss the equivalence between these two models in the low-lying sector and realize these anyon excitations in a conventional fermion system.

cond-mat.stat-mech↗
arXiv2010

Supersymmetric Response of Bose-Fermi Mixture to Photoassociation

We study supersymmetric (SUSY) responses to a photoassociation process in a mixture of Bose molecules $b$ and Fermi atoms $f$ which turn to mutual superpartners for a set of proper parameters. We consider the molecule $b$ to be a bound state of the atom $f$ and another Fermi atom $F$ with different species. The $b$-$f$ mixture and a free $F$ atom gas are loaded in an optical lattice. The SUSY nature of the mixture can be signaled in the response to a photon induced atom-molecule transition: While two new types of fermionic excitations, an individual $b$ particle-$f$ hole pair continuum and the Goldstino-like collective mode, are concomitant for a generic $b$-$f$ mixture, the former is completely suppressed in the SUSY $b$-$f$ mixture and the zero-momentum mode of the latter approaches to an exact eigenstate. This SUSY response can be detected by means of the spectroscopy method, e.g., the photoassociation spectrum which displays the molecular formation rate of $% Ff\to b$.

cond-mat.other↗
arXiv2009

Quantized squeezing and even-odd asymmetry of trapped bosons

We investigate the exact nature of the superfluid-to-Mott-insulator crossover for interacting bosons on an optical lattice in a one-dimensional, harmonic trap by high-precision density-matrix renormalization-group calculations. The results reveal an intermediate regime characterized by a cascade of microscopic steps. These arise as a consequence of individual boson "squeezing" events and display an even-odd alternation dependent on the trap symmetry. We discuss the experimental observation of this behavior, which is generic in an external trapping potential.

cond-mat.quant-gas↗
arXiv2009

Anyons from fermions with conventional two-body interactions

Emergent anyons are the key elements of the topological quantum computation and topological quantum memory. We study a two-component fermion model with conventional two-body interaction in an open boundary condition and show that several subsets in the low-lying excitations obey the same fusion rules as those of the toric code model. Those string-like non-local excitations in a given subset obey mutual semionic statistics. We show how to peel off one of such subset from other degenerate subsets and manipulate anyons in cold dipolar Fermi atoms or cold dipolar fermionic heteronuclear molecules in optical lattices by means of the established techniques.

cond-mat.other↗
arXiv2009

Topological quantum phase transition in an extended Kitaev spin model

We study the quantum phase transition between Abelian and non-Abelian phases in an extended Kitaev spin model on the honeycomb lattice, where the periodic boundary condition is applied by placing the lattice on a torus. Our analytical results show that this spin model exhibits a continuous quantum phase transition. Also, we reveal the relationship between bipartite entanglement and the ground-state energy. Our approach directly shows that both the entanglement and the ground-state energy can be used to characterize the topological quantum phase transition in the extended Kitaev spin model.

cond-mat.stat-mech↗
arXiv2009

An exactly soluble model with tunable p-wave paired fermion ground states

Motivated by the work of Kitaev, we construct an exactly soluble spin-$\frac{1}2$ model on honeycomb lattice whose ground states are identical to $Δ_{1x}p_x+Δ_{1y}p_y+i(Δ_{2x}p_x+Δ_{2y}p_y)$-wave paired fermions on square lattice, with tunable paring order parameters. We derive a universal phase diagram for this general p-wave theory which contains a gapped A phase and a topologically non-trivial B phase. We show that the gapless condition in the B phase is governed by a generalized inversion (G-inversion) symmetry under $p_x\leftrightarrow {Δ_{1y}\over Δ_{1x}} p_y$. The G-inversion symmetric gapless B phase near the phase boundaries is described by 1+1-dimensional gapless Majorana fermions in the asymptotic long wave length limit, i.e. the $c=1/2$ conformal field theory. The gapped B phase has G-inversion symmetry breaking and is the weak pairing phase described by the Moore-Read Pfaffian. We show that in the gapped B phase, vortex pair excitations are separated from the ground state by a finite energy gap.

cond-mat.str-el↗
arXiv2008

Explicit illustration of non-abelian fusion rules in a small spin lattice

We exactly solve a four-site spin model with site-dependent Kitaev's coupling in a tetrahedron by means of an analytical diagonalization. The non-abelian fusion rules of eigen vortex excitations in this small lattice model are explicitly illustrated in real space by using Pauli matrices. Comparing with solutions of Kitaev models on large lattices, our solution gives an intuitional picture using real space spin configurations to directly express zero modes of Majorana fermions, non-abelian vortices and non-abelian fusion rules. We generalize the single tetrahedron model to a chain model of tetrahedrons on a torus and find the non-abelian vortices become well-defined non-abelian anyons. We believe these manifest results are very helpful to demonstrate the nonabelian anyon in laboratory.

cond-mat.str-el↗
arXiv2008

Solitons and vortices in an evolving Bose-Einstein condensate

Spatiotemporal evolution of a confined Bose-Einstein condensate is studied by numerically integrating the time-dependent Gross-Pitaevskii equation. Self-interference between the successively expanding and reflecting nonlinear matter waves results in spiral atomic density profile, which subsequently degenerates into an embedding structure: The inner part preserves memory of the initial states while the outer part forms a sequence of necklacelike rings. The phase plot reveals a series of discrete concentric belts. The large gradients between adjacent belts indicate that the ring density notches are dark solitons. In the dynamical process, a scenario of vortex-antivortex pairs are spontaneously created and annihilated, whereas the total vorticity keeps invariant.

cond-mat.supr-con↗
arXiv2008

Anyonic Loops in Three Dimensional Spin liquid and Chiral Spin Liquid

We established a large class of exactly soluble spin liquids and chiral spin liquids on three dimensional helix lattices by introducing Kitaev-type's spin coupling. In the chiral spin liquids, exact stable ground states with spontaneous breaking of the time reversal symmetry are found. The fractionalized loop excitations in both the spin and chiral spin liquids obey non-abelian statistics. We characterize this kind of statistics by non-abelian Berry phase and quantum algebra relation. The topological correlation of loops is independent of local order parameter and it measures the intrinsic global quantum entanglement of degenerate ground states.

cond-mat.str-el↗
arXiv2008

Explicit demonstration of nonabelian anyon, braiding matrix and fusion rules in the Kitaev-type spin honeycomb lattice models

The exact solubility of the Kitaev-type spin honeycomb lattice model was proved by means of a Majorana fermion representation or a Jordan-Wigner transformation while the explicit form of the anyon in terms of Pauli matrices became not transparent. The nonabelian statistics of anyons and the fusion rules can only be expressed in indirect ways to Pauli matrices. We convert the ground state and anyonic excitations back to the forms of Pauli matrices and explicitly demonstrate the nonabelian anyonic statistics as well as the fusion rules. These results may instruct the experimental realization of the nonabelian anyons. We suggest a proof-in-principle experiment to verify the existence of the nonabelian anyons in nature.

cond-mat.stat-mech↗
arXiv2008

Supersymmetry and Goldstino-like Mode in Bose-Fermi Mixtures

Supersymmetry is assumed to be a basic symmetry of the world in many high energy theories, but none of the super partners of any known elementary particle has been observed yet. We argue that supersymmetry can also be realized and studied in ultracold atomic systems with a mixture of bosons and fermions, with properly tuned interactions and single particle dispersion. We further show that in such non-releativistic systems supersymmetry is either spontaneously broken, or explicitly broken by a chemical potential difference between the bosons and fermions. In both cases the system supports a sharp fermionic collective mode or the so-called Goldstino, due to supersymmetry. We also discuss possible ways to detect the Goldstino mode experimentally.

cond-mat.other↗
arXiv2008

Quaternate generalization of Pfaffian state at $ν=5/2$

We consider a quaternately generalized Pfaffian QGPf$(\frac{1}{J(z_i,z_j,z_k,z_l)})[J(z_1,...,z_N)]^2$ in which the square of Vandermonde determinant, $[J(z_1,...,z_N)]^2$, implies the upmost Landau level is half filled. This wave function is the unique highest density zero energy state of a special short range interacting Hamiltonian. One can think this quaternate composite fermion liquid as a competing ground state of Moore-Read (MR) Pfaffian state at $ν=5/2$. The degeneracy of the quasihole excitations above the QGPf is higher than that of Moore-Read even Read-Rezayi quasiholes. The QGPf is related to a unitary conformal field theory with $Z_2\times Z_2$ parafermions in coset space $SU(3)_2/U(1)^2$ . Because of the level-rank duality between $SU(3)_2$ and $SU(2)_3$ in conformal field theory, these quasiholes above this QGPf state obeying non-abelian anyonic statistics are expected to support the universal quantum computation at $ν=5/2$ as Read-Rezayi quasiholes at $ν=13/5$. The edge states of QGPf are very different from those of the Pfaffian's.

cond-mat.mes-hall↗
arXiv2008

Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds

We construct an exactly soluble spin-$\frac{1}2$ model on a honeycomb lattice, which is a generalization of Kitaev model. The topological phases of the system are analyzed by study of the ground state sector of this model, the vortex-free states. Basically, there are two phases, A phase and B phase. The behaviors of both A and B phases may be studied by mapping the ground state sector into a general p-wave paired states of spinless fermions with tunable pairing parameters on a square lattice. In this p-wave paired state theory, the A phase is shown to be the strong paired phase, an insulating phase. The B phase may be either gapped or gapless determined by the generalized inversion symmetry is broken or not. The gapped B is the weak pairing phase described by either the Moore-Read Pfaffian state of the spinless fermions or anti-Pfaffian state of holes depending on the sign of the next nearest neighbor hopping amplitude. A phase transition between Pfaffian and anti-Pfaffian states are found in the gapped B phase. Furthermore, we show that there is a hidden SU(2) gauge symmetry in our model. In the gapped B phase, the ground state has a non-trivial topological number, the spectral first Chern number or the chiral central charge, which reflects the chiral anomaly of the edge state. We proved that the topological number is identified to the reduced eta-invariant and this anomaly may be cancelled by a bulk Wess-Zumino term of SO(3) group through an index theorem in 2+1 dimensions.

cond-mat.str-el↗