arXiv subjects

Long Liang

Publications and source records attributed to Long Liang.

28 records · Page 2Linked to original sources

arXiv2017

Band geometry, Berry curvature and superfluid weight

We present a theory of the superfluid weight in multiband attractive Hubbard models within the Bardeen-Cooper-Schrieffer (BCS) mean field framework. We show how to separate the geometric contribution to the superfluid weight from the conventional one, and that the geometric contribution is associated with the interband matrix elements of the current operator. Our theory can be applied to systems with or without time reversal symmetry. In both cases the geometric superfluid weight can be related to the quantum metric of the corresponding noninteracting systems. This leads to a lower bound on the superfluid weight given by the absolute value of the Berry curvature. We apply our theory to the attractive Kane-Mele-Hubbard and Haldane-Hubbard models, which can be realized in ultracold atom gases. Quantitative comparisons are made to state of the art dynamical mean-field theory and exact diagonalization results.

cond-mat.supr-con↗

arXiv2016

Doublon-holon binding as origin of Mott transition and fractionalized spin liquid -- Asymptotic solution of the Hubbard model in the limit of large coordination

An analytical solution of the Mott transition is obtained for the Hubbard model on the Bethe lattice in the large coordination number ($z$) limit. The excitonic binding of doublons (doubly occupied sites) and holons (empty sites) is shown to be the origin of a continuous Mott transition between a metal and an emergent quantum spin liquid insulator. The doublon-holon binding theory enables a different large-$z$ limit and a different phase structure than the dynamical meanfield theory by allowing intersite spinon correlations to lift the $2^N$-fold degeneracy of the local moments in the insulating phase. We show that the spinons are coupled to doublons/holons by a dissipative compact U(1) gauge field that is in the deconfined phase, stabilizing the spin-charge separated gapless spin liquid Mott insulator.

cond-mat.str-el↗

arXiv2016

Topological phase transitions in the repulsively interacting Haldane-Hubbard model

Using dynamical mean-field theory and exact diagonalization we study the phase diagram of the repulsive Haldane-Hubbard model, varying the interaction strength and the sublattice potential difference. In addition to the quantum Hall phase with Chern number $C=2$ and the band insulator with $C=0$ present already in the noninteracting model, the system also exhibits a $C=0$ Mott insulating phase, and a $C=1$ quantum Hall phase. We explain the latter phase by a spontaneous symmetry breaking where one of the spin-components is in the Hall state and the other in the band insulating state.

cond-mat.quant-gas↗

arXiv2015

Heterogeneous Force Chains in Cellularized Biopolymer Network

Biopolymer Networks play an important role in coordinating and regulating collective cellular dynamics via a number of signaling pathways. Here, we investigate the mechanical response of a model biopolymer network due to the active contraction of embedded cells. Specifically, a graph (bond-node) model derived from confocal microscopy data is used to represent the network microstructure, and cell contraction is modeled by applying correlated displacements at specific nodes, representing the focal adhesion sites. A force-based stochastic relaxation method is employed to obtain force-balanced network under cell contraction. We find that the majority of the forces are carried by a small number of heterogeneous force chains emitted from the contracting cells. The force chains consist of fiber segments that either possess a high degree of alignment before cell contraction or are aligned due to the reorientation induced by cell contraction. Large fluctuations of the forces along different force chains are observed. Importantly, the decay of the forces along the force chains is significantly slower than the decay of radially averaged forces in the system. These results suggest that the fibrous nature of biopolymer network structure can support long-range force transmission and thus, long-range mechanical signaling between cells.

cond-mat.soft↗

arXiv2015

Rarita-Schwinger-Weyl semimetal in Jeff=3/2 electron systems

We propose a relativistic Jeff=3/2 semimetal with 4d1 or 5d1 electrons on a cubic lattice when the strong spin-orbital coupling takes over the Hunds' coupling. A relativistic spinor with spin 3/2 is historically called Rarita-Schwinger spinor. In the massless case, the right- and left-handed chiral degrees of freedom of the Rarita-Schwinger spinors are independent. In the lattice model that we propose, the right- and left- handed gapless points in Brillouin zone are separated. We call this linearly dispersed semimetal Rarita-Schwinger-Weyl semimetal, similar to Weyl semimetal for spin 1/2 systems. There is a network of gapless Fermi arcs in the surface Brillouin zone if n1+n2+n3 is even for the normal vector (n1,n2,n3) of the surface while the surface is insulator if n1+n2+n3 is odd.

cond-mat.mes-hall↗

arXiv2015

Collective modes in a Dirac insulator with short range interactions

We study a Haldane model with nearest neighbor interactions. We find one-dimensional like collective modes arising due to the interplay of pseudo-spin and valley degrees of freedom. In the large band gap or moderate interaction limit, these excitations are low energy modes lying in the band gap. The dispersion relations are qualitatively different in trivial insulator phase and Chern insulator phase, thus can be used to identify the topology of the Haldane model with the bulk property. We also discuss how to detect these modes in cold atom systems. An abelian gauge theory will emerge when a physical current-current interaction is introduced to the Haldane model or the Kane-Mele model.

cond-mat.str-el↗

arXiv2015

Global Phase Diagram of the Extended Kitaev-Heisenberg Model on Honeycomb Lattice

We study the extended Kitaev-Heisenberg (EKH) quantum spin model by adding bond-dependent off-diagonal Heisenberg term into the original KH model, which was recently proposed to describe the honeycomb Iridates. A rigorous mathematical mapping of spin operators reveals the intrinsic symmetry of the model Hamiltonian. By employing an unbiased numerical entanglement renormalization method based on tensor network ansatz, we obtain the global phase diagram containing eight distinct quantum phases. By using the dual mapping of spin operators, each of the individual magnetic phase in the global phase diagram can be clearly understood. At last, we show that a valence solid state emerges as the ground state in the quadro-critical region where multiple magnetic phases compete most intensively.

cond-mat.str-el↗

arXiv2014

Distinct-symmetry spin liquid states and phase diagram of Kitaev-Hubbard model

We report the finding of a series of symmetry distinct spin liquid (SL) states and a rich phase diagram in a half-filled honeycomb lattice Hubbard model with spin-dependent hopping amplitude t'. We first study the magnetic instability of the system and find two antiferromagnetic orders beyond a critical Hubbard U which increases with the ratio t'/t . For $t'$ approaching to $t$, the semimetal (SM) transforms to a U(1) SL and then to the Kitaev Z_2 SL as U increases. In a wide middle range of t'/t, the latter is replaced by a U(1) SL to $SU(2)$ SL transition. The physical properties of the stable SL phases are discussed.

cond-mat.str-el↗

arXiv2013

Tuning into the Kitaev spin liquid phase:A spin model on the honeycomb lattice with two types of Heisenberg exchange couplings

We study a spin model on honeycomb lattice with two types of Heisenberg exchange couplings, $J$ and $\tilde J$, where $J$ is for the conventional spin and and $\tilde J$ for rotated spin. When $\tilde J=0$, this is the conventional Heisenberg model. When J=0, the system is either in a stripy antiferromagnetic order($\tilde J<0$, ferromagnetic for rotated spin) or a zig-zag antiferromagnetic order ($\tilde J>0$, antiferromagnetic for rotated spin). The competition between two ferromagnetic orders or two antiferromagnetic orders induces Kitaev's spin liquid phase characterized by the exactly solvable Kitaev model ($J=\tilde J$). Our model can be applied to layered Mott insulators A$_2$IrO$_3$ (A=Li, Na). For a monolayer of Li$_2$IrO$_3$, we show that it is possible to tune the controlling parameter into the Kitaev spin liquid regime by a link-dependent Rashba spin-orbital coupling.

cond-mat.str-el↗

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↗