arXiv subjects

Congjun Wu

Publications and source records attributed to Congjun Wu.

At least 109 records · Page 6Linked to original sources

arXiv2016

3D quaternionic condensations, Hopf invariants, and skyrmion lattices with synthetic spin-orbit coupling

We study the topological configurations of the two-component condensates of bosons with the $3$D $\vecσ\cdot \vec{p}$ Weyl-type spin-orbit coupling subject to a harmonic trapping potential. The topology of the condensate wavefunctions manifests in the quaternionic representation. In comparison to the $U(1)$ complex phase, the quaternionic phase manifold is $S^3$ and the spin orientations form the $S^2$ Bloch sphere through the 1st Hopf mapping. The spatial distributions of the quaternionic phases exhibit the 3D skyrmion configurations, and the spin distributions possess non-trivial Hopf invariants. Spin textures evolve from the concentric distributions at the weak spin-orbit coupling regime to the rotation symmetry breaking patterns at the intermediate spin-orbit coupling regime. In the strong spin-orbit coupling regime, the single-particle spectra exhibit the Landau-level type quantization. In this regime, the three-dimensional skyrmion lattice structures are formed when interactions are below the energy scale of Landau level mixings. Sufficiently strong interactions can change condensates into spin-polarized plane-wave states, or, superpositions of two plane-waves exhibiting helical spin spirals.

cond-mat.quant-gas↗

arXiv2015

Mott insulating states and quantum phase transitions of correlated SU(2N) Dirac fermions

The interplay between charge and spin degrees of freedom in strongly correlated fermionic systems, in particular of Dirac fermions, is a long-standing problem in condensed matter physics. We investigate the competing orders in the half-filled SU(2N) Hubbard model on a honeycomb lattice, which can be accurately realized in optical lattices with large-spin ultra-cold alkaline-earth fermions. Employing large-scale projector determinant quantum Monte Carlo simulations, we have explored quantum phase transitions from the gapless Dirac semi-metals to the gapped Mott-insulating phases in the SU(4) and SU(6) cases. Both of these Mott-insulating states are found to be columnar valence bond solid (cVBS) and to be absent of the antiferromagnetic Neel ordering and the loop current ordering. Inside the cVBS phases, the dimer ordering is enhanced by increasing fermion components and behaves non-monotonically as the interaction strength increases. Although the transitions generally should be of first order due to a cubic invariance possessed by the cVBS order, the coupling to gapless Dirac fermions can soften the transitions to second order through a non-analytic term in the free energy. Our simulations provide important guidance for the experimental exploration of novel states of matter with ultra-cold alkaline earth fermions.

cond-mat.quant-gas↗

arXiv2015

Sign problem free quantum Monte-Carlo study on thermodynamic properties and magnetic phase transitions in orbital-active itinerant ferromagnets

The microscopic mechanism of itinerant ferromagnetism is a long-standing problem due to the lack of non-perturbative methods to handle strong magnetic fluctuations of itinerant electrons. We have non-pertubatively studied thermodynamic properties and magnetic phase transitions of a two-dimensional multi-orbital Hubbard model exhibiting ferromagnetic ground states. Quantum Monte-Carlo simulations are employed, which are proved in a wide density region free of the sign problem usually suffered by simulations for fermions. Both Hund's coupling and electron itinerancy are essential for establishing the ferromagnetic coherence. No local magnetic moments exist in the system as a priori, nevertheless, the spin channel remains incoherent showing the Curie-Weiss type spin magnetic susceptibility down to very low temperatures at which the charge channel is already coherent exhibiting a weakly temperature-dependent compressibility. For the SU(2) invariant systems, the spin susceptibility further grows exponentially as approaching zero temperature in two dimensions. In the paramagnetic phase close to the Curie temperature, the momentum space Fermi distributions exhibit strong resemblance to those in the fully polarized state. The long-range ferromagnetic ordering appears when the symmetry is reduced to the Ising class, and the Curie temperature is accurately determined. These simulations provide helpful guidance to searching for novel ferromagnetic materials in both strongly correlated $d$-orbital transition metal oxide layers and the $p$-orbital ultra-cold atom optical lattice systems.

cond-mat.str-el↗

arXiv2015

Detecting edge degeneracy in interacting topological insulators through entanglement entropy

The existence of degenerate or gapless edge states is a characteristic feature of topological insulators, but is difficult to detect in the presence of interactons. We propose a new method to obtain the degeneracy of the edge states from the perspective of entanglement entropy, which is very useful to identify interacting topological states. Employing the determinant quantum Monte Carlo technique, we investigate the interaction effect on two representative models of fermionic topological insulators in one and two dimensions, respectively. In the two topologically nontrivial phases, the edge degeneracies are reduced by interactions but remain to be nontrivial.

cond-mat.str-el↗

arXiv2015

Unconventional symmetries of Fermi liquid and Cooper pairing properties with electric and magnetic dipolar fermions

The rapid experimental progress of ultra-cold dipolar fermions opens up a whole new opportunity to investigate novel many-body physics of fermions. In this article, we review theoretical studies of the Fermi liquid theory and Cooper pairing instabilities of both electric and magnetic dipolar fermionic systems from the perspective of unconventional symmetries. When the electric dipole moments are aligned by the external electric field, their interactions exhibit the explicit $d_{r^2-3z^2}$ anisotropy. The Fermi liquid properties, including the single-particle spectra, thermodynamic susceptibilities, and collective excitations, are all affected by this anisotropy. The electric dipolar interaction provides a mechanism for the unconventional spin triplet Cooper pairing, which is different from the usual spin-fluctuation mechanism in solids and the superfluid $^3$He. Furthermore, the competition between pairing instabilities in the singlet and triplet channels gives rise to a novel time-reversal symmetry breaking superfluid state. Unlike electric dipole moments which are induced by electric fields and unquantized, magnetic dipole moments are intrinsic proportional to the hyperfine-spin operators with a Lande factor. Its effects even manifest in unpolarized systems exhibiting an isotropic but spin-orbit coupled nature. The resultant spin-orbit coupled Fermi liquid theory supports a collective sound mode exhibiting a topologically non-trivial spin distribution over the Fermi surface. It also leads to a novel $p$-wave spin triplet Cooper pairing state whose spin and orbital angular momentum are entangled to the total angular momentum $J=1$ dubbed the $J$-triplet pairing. This $J$-triplet pairing phase is different from both the spin-orbit coupled $^3$He-$B$ phase with $J=0$ and the spin-orbit decoupled $^3$He-$A$ phase.

cond-mat.quant-gas↗

arXiv2014

The in-plane gradient magnetic field induced vortex lattices in spin-orbit coupled Bose-Einstein condensations

We consider the ground-state properties of the two-component spin-orbit coupled ultracold bosons subject to a rotationally symmetric in-plane gradient magnetic field. In the non-interacting case, the ground state supports giant-vortices carrying large angular momenta without rotating the trap. The vorticity is highly tunable by varying the amplitudes and orientations of the magnetic field. Interactions drive the system from a giant-vortex state to various configurations of vortex lattice states along a ring. Vortices exhibit ellipse-shaped envelops with the major and minor axes determined by the spin-orbit coupling and healing lengths, respectively. Phase diagrams of vortex lattice configurations are constructed and their stabilities are analyzed.

cond-mat.quant-gas↗

arXiv2014

Quantum Monte Carlo simulation of thermodynamic properties of SU(2N) ultracold fermions in optical lattices

We have systematically studied the thermodynamic properties of a two-dimensional half-filled SU(2N) Hubbard model on a square lattice by using the determinant quantum Monte Carlo method. The entropy-temperature relation, the isoentropy curve, and the probability distribution of the onsite occupation number are calculated in both SU(4) and SU(6) cases, which exhibit prominent features of the Pomeranchuk effect. We analyze these thermodynamic behaviors based on charge and spin energy scales. In the charge channel, the interaction strength that marks the crossover from the weak to strong interaction regimes increases with the number of fermion components. In the spin channel, increasing the number of fermion components enhances quantum spin fluctuations, which is shown in the simulations of uniform spin susceptibilities and antiferromagnetic structure factors.

cond-mat.quant-gas↗

arXiv2014

The honeycomb lattice with multi-orbital structure: topological and quantum anomalous Hall insulators with large gaps

We construct a minimal four-band model for the two-dimensional (2D) topological insulators and quantum anomalous Hall insulators based on the $p_x$- and $p_y$-orbital bands in the honeycomb lattice. The multiorbital structure allows the atomic spin-orbit coupling which lifts the degeneracy between two sets of on-site Kramers doublets $j_z=\pm\frac{3}{2}$ and $j_z=\pm\frac{1}{2}$. Because of the orbital angular momentum structure of Bloch-wave states at $Γ$ and $K(K^\prime)$ points, topological gaps are equal to the atomic spin-orbit coupling strengths, which are much larger than those based on the mechanism of the $s$-$p$ band inversion. In the weak and intermediate regime of spin-orbit coupling strength, topological gaps are the global gap. The energy spectra and eigen wave functions are solved analytically based on Clifford algebra. The competition among spin-orbit coupling $λ$, sublattice asymmetry $m$ and the Néel exchange field $n$ results in band crossings at $Γ$ and $K (K^\prime)$ points, which leads to various topological band structure transitions. The quantum anomalous Hall state is reached under the condition that three gap parameters $λ$, $m$, and $n$ satisfy the triangle inequality. Flat bands also naturally arise which allow a local construction of eigenstates. The above mechanism is related to several classes of solid state semiconducting materials.

cond-mat.mes-hall↗

arXiv2014

The fate and heir of Majorana zero modes in a quantum wire array

Experimental signatures of Majorana zero modes in a single superconducting quantum wire with spin-orbit coupling have been reported as zero bias peaks in the tunneling spectroscopy. We study whether these zero modes can persist in an array of coupled wires, and if not, what their remnant could be. The bulk exhibits topologically distinct gapped phases and an intervening gapless phase. Even though the bulk pairing structure is topological, the interaction between Majorana zero modes and superfluid phases leads to spontaneous time-reversal symmetry breaking. Consequently, edge supercurrent loops emerge and edge Majorana fermions are in general gapped out except when the number of chains is odd, in which case one Majorana fermion survives.

cond-mat.mes-hall↗

arXiv2014

Exact Results on Itinerant Ferromagnetism in Multi-orbital Systems on Square and Cubic Lattices

We study itinerant ferromagnetism in multi-orbital Hubbard models in certain two-dimensional square and three-dimensional cubic lattices. In the strong coupling limit where doubly occupied orbitals are not allowed, we prove that the fully spin-polarized states are the unique ground states, apart from the trivial spin degeneracies, for a large region of fillings factors. Possible applications to p-orbital bands with ultra-cold fermions in optical lattices, and electronic 3d-orbital bands in transition-metal oxides, are discussed.

cond-mat.str-el↗

arXiv2014

Competing orders in the 2D half-filled SU(2N) Hubbard model through the pinning field quantum Monte-Carlo simulations

We non-perturbatively investigate the ground state magnetic properties of the 2D half-filled SU($2N$) Hubbard model in the square lattice by using the projector determinant quantum Monte Carlo simulations combined with the method of local pinning fields. Long-range Neel orders are found for both the SU(4) and SU(6) cases at small and intermediate values of $U$. In both cases, the long-range Neel moments exhibit non-monotonic behavior with respect to $U$, which first grow and then drop as $U$ increases. This result is fundamentally different from the SU(2) case in which the Neel moments increase monotonically and saturate. In the SU(6) case, a transition to the columnar dimer phase is found in the strong interaction regime.

cond-mat.str-el↗

arXiv2013

Four-coloring model and frustrated superfluidity in the diamond lattice

We propose a novel four-coloring model which describes "frustrated superfluidity" of $p$-band bosons in the diamond optical lattice. The superfluid phases of the condensate wavefunctions on the diamond-lattice bonds are mapped to four distinct colors at low temperatures. The fact that a macroscopic number of states satisfy the constraints that four differently colored bonds meet at the same site leads to an extensive degeneracy in the superfluid ground state at the classical level. We demonstrate that the phase of the superfluid wavefunction as well as the orbital angular momentum correlations exhibit a power-law decay in the degenerate manifold that is described by an emergent magnetostatic theory with three independent flux fields. Our results thus provide a novel example of critical superfluid phase with algebraic order in three dimensions. We further show that quantum fluctuations favor a Néel ordering of orbital angular moments with broken sublattice symmetry through the order-by-disorder mechanism.

cond-mat.str-el↗

arXiv2013

Topological insulators with SU(2) Landau levels

We construct continuum models of 3D and 4D topological insulators by coupling spin-1/2 fermions to an SU(2) background gauge field, which is equivalent to a spatially dependent spin-orbit coupling. Higher dimensional generalizations of flat Landau levels are obtained in the Landau-like gauge. The 2D helical Dirac modes with opposite helicities and 3D Weyl modes with opposite chiralities are spatially separated along the third and fourth dimensions, respectively. Stable 2D helical Fermi surfaces and 3D chiral Fermi surfaces appear on open boundaries, respectively. The charge pumping in 4D Landau level systems shows quantized 4D quantum Hall effect.

cond-mat.str-el↗

arXiv2013

Spontaneous time-reversal symmetry breaking in the boundary Majorana flat bands

We study the boundary Majorana modes for the single component p-wave weak topological superconductors or superfluids, which form zero energy flat bands protected by time-reversal symmetry in the orbital channel. However, due to the divergence of density of states, the band flatness of the edge Majorana modes is unstable under spontaneously generated spatial variations of Cooper pairing phases. Staggered current loops appear near the boundary and thus time-reversal symmetry is spontaneously broken in the orbital channel. This effect can appear in both condensed matter and ultra-cold atom systems.

cond-mat.supr-con↗

arXiv2013

Unconventional states of bosons with synthetic spin-orbit coupling

Spin-orbit coupling with bosons gives rise to novel properties that are absent in usual bosonic systems. Under very general conditions, the conventional ground state wavefunctions of bosons are constrained by the "no-node" theorem to be positive-definite. In contrast, the linear-dependence of spin-orbit coupling leads to complex-valued condensate wavefunctions beyond this theorem. In this article, we review the study of this class of unconventional Bose-Einstein condensations focusing on their topological properties. Both the 2D Rashba and 3D $\vecσ \cdot \vec{p}$-type Weyl spin-orbit couplings give rise to Landau-level-like quantization of single-particle levels in the harmonic trap. The interacting condensates develop the half-quantum vortex structure spontaneously breaking time-reversal symmetry and exhibit topological spin textures of the skyrmion type. In particular, the 3D Weyl coupling generates topological defects in the quaternionic phase space as an SU(2) generalization of the usual U(1) vortices. Rotating spin-orbit coupled condensates exhibit rich vortex structures due to the interplay between vorticity and spin texture. In the Mott-insulating states in optical lattices, quantum magnetism is characterized by the Dzyaloshinskii-Moriya type exchange interactions.

cond-mat.quant-gas↗

arXiv2013

Pomeranchuk cooling of the SU($2N$) ultra-cold fermions in optical lattices

We investigate the thermodynamic properties of a half-filled SU(2N) Fermi-Hubbard model in the two-dimensional square lattice using the determinantal quantum Monte Carlo simulation, which is free of the fermion "sign problem". The large number of hyperfine-spin components enhances spin fluctuations, which facilitates the Pomeranchuk cooling to temperatures comparable to the superexchange energy scale at the case of SU$(6)$. Various quantities including entropy, charge fluctuation, and spin correlations have been calculated.

cond-mat.quant-gas↗

arXiv2013

High-Dimensional Topological Insulators with Quaternionic Analytic Landau Levels

We study the 3D topological insulators in the continuum by coupling spin-1/2 fermions to the Aharonov-Casher SU(2) gauge field. They exhibit flat Landau levels in which orbital angular momentum and spin are coupled with a fixed helicity. The 3D lowest Landau level wavefunctions exhibit the quaternionic analyticity as a generalization of the complex analyticity of the 2D case. Each Landau level contributes one branch of gapless helical Dirac modes to the surface spectra, whose topological properties belong to the Z2-class. The flat Landau levels can be generalized to an arbitrary dimension. Interaction effects and experimental realizations are also studied.

cond-mat.str-el↗

arXiv2013

Magnetic phases of bosons with synthetic spin-orbit coupling in optical lattices

We investigate magnetic properties in the superfluid and Mott-insulating states of two-component bosons with spin-orbit (SO) coupling in 2D square optical lattices. The spin-independent hopping integral $t$ and SO coupled one $λ$are fitted from band structure calculations in the continuum, which exhibit oscillations as increasing SO coupling strength. The magnetic superexchange model is derived in the Mott-insulating state with one-particle per-site, characterized by the Dzyaloshinsky-Moriya (DM) interaction. In the limit of $|λ|\ll |t|$, we find a spin spiral Mott state whose pitch value is the same as that in the incommensurate superfluid state, while in the opposite limit $|t| \ll |λ|$, the ground state can be found by a dual transformation to the $|λ|\ll|t|$ limit.

cond-mat.quant-gas↗