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arXiv2014

Patterns of Genuine Multipartite Entanglement in Frustrated Quantum Spin Systems

We investigate the behavior of genuine multipartite entanglement of paradigmatic frustrated quantum spin systems. We consider six different spin models, whose frustration ranges from being very high to very low. We find that the highly frustrated quantum spin systems are near-maximally genuine multipartite entangled, while those with low frustration do not possess a similar definite behavior with regard to their genuine multipartite entanglement.

quant-ph↗

arXiv2013

Ising models and topological codes: classical algorithms and quantum simulation

We present an algorithm to approximate partition functions of 3-body classical Ising models on two-dimensional lattices of arbitrary genus, in the real-temperature regime. Even though our algorithm is purely classical, it is designed by exploiting a connection to topological quantum systems, namely the color codes. The algorithm performance is exponentially better than other approaches which employ mappings between partition functions and quantum state overlaps. In addition, our approach gives rise to a protocol for quantum simulation of such Ising models by simply measuring local observables on color codes.

quant-ph↗

arXiv2013

Optimal multi-configuration approximation of an N-fermion wave function

We propose a simple iterative algorithm to construct the optimal multi-configuration approximation of an $N$-fermion wave function. That is, $M\geq N $ single-particle orbitals are sought iteratively so that the projection of the given wave function in the $C_M^N$-dimensional configuration subspace is maximized. The algorithm has a monotonic convergence property and can be easily parallelized. The significance of the algorithm on the study of entanglement in a multi-fermion system and its implication on the multi-configuration time-dependent Hartree-Fock (MCTDHF) are discussed. The ground state and real-time dynamics of spinless fermions with nearest-neighbor interactions are studied using this algorithm, discussing several subtleties.

quant-ph↗

arXiv2013

Topological phases in small quantum Hall samples

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect. One way to detect is via direct observation of anyonic properties of excitations which are usually discussed in the thermodynamic limit, but so far has not been realized in macroscopic quantum Hall samples. Here we consider a system of few interacting bosons subjected to the lowest Landau level by a gauge potential, and theoretically investigate vortex excitations in order to identify topological properties of different ground states. Our investigation demonstrates that even in surprisingly small systems anyonic properties are able to characterize the topological order. In addition, focusing on a system in the Laughlin state, we study the robustness of its anyonic behavior in the presence of tunable finite-range interactions acting as a perturbation. A clear signal of a transition to a different state is reflected by the system's anyonic properties.

cond-mat.quant-gas↗

arXiv2014

Two-species hard-core bosons on the triangular lattice: A quantum Monte Carlo study

Using worm-type quantum Monte Carlo simulations, we investigate bosonic mixtures on the triangular lattice of two species of bosons, which interact via nearest-neighbour intraspecies ($V$) and onsite interspecies ($U$) repulsions. For the case of symmetric hopping amplitude ($t_A/V=t_B/V$) and $U/V=1$, we determine a rich ground-state phase diagram that contains double solid, double superfluid (2SF), supersolid (SS), solid-superfluid (Solid-SF) and counterflow supersolid (CSS) states. The SS, Solid-SF and CSS states exhibit spontaneous symmetry breaking among the three sublattices of the triangular lattice and between the two species, which leads to nonzero crystalline density wave order in each species. We furthermore show that the CSS and the SS states are present for $t_A/V \neq t_B/V$, and the latter even survives up to $t_A/V \rightarrow \infty$ or $t_B/V \rightarrow \infty$ limit. The effects induced by the variation of $U/V$ and by the imbalance of particle numbers of the two species are also explored.

cond-mat.quant-gas↗

arXiv2014

Theoretical Description of Coherent Doublon Creation via Lattice Modulation Spectroscopy

Using a recently developed strong-coupling method, we present a comprehensive theory for doublon production processes in modulation spectroscopy of a three-dimensional system of ultracold fermionic atoms in an optical lattice with a trap. The theoretical predictions compare well to the experimental time traces of doublon production. For experimentally feasible conditions, we provide a quantitative prediction for the presence of a nonlinear "two-photon" excitation at strong modulation amplitudes.

cond-mat.str-el↗

arXiv2014

Unconventional superfluidity in quasi-one-dimensional systems

We show that an unconventional superfluid triggered by spin-orbit coupling is realized for repulsively interacting quasi-one-dimensional fermions. A competition between spin-singlet and -triplet pairings occurs due to the breaking of inversion symmetry. We show that both superfluid correlations decay algebraically with the same exponent except for special coupling constants for which a dominant superfluid is controlled by the spin-orbit coupling. We also discuss a possible experiment to observe such phases with cold atoms.

cond-mat.quant-gas↗

arXiv2014

Noncompact dynamical symmetry of a spin-orbit coupled oscillator

We explain the finite as well as infinite degeneracy in the spectrum of a particular system of spin-1/2 fermions with spin-orbit coupling in three spatial dimensions. Starting from a generalized Runge-Lenz vector, we explicitly construct a complete set of symmetry operators, which span a noncompact SO(3,2) algebra. The degeneracy of the physical spectrum only involves a particular, infinite, so called singleton representation. In the branch where orbital and spin angular momentum are aligned the full representation appears, constituting a 3D analogue of Landau levels. Anti-aligning the spin leads to a finite degeneracy due to a truncation of the singleton representation. We conclude the paper by constructing the spectrum generating algebra of the problem.

cond-mat.mes-hall↗

arXiv2013

Shared Purity of Multipartite Quantum States

Fidelity plays an important role in measuring distances between pairs of quantum states, of single as well as multiparty systems. Based on the concept of fidelity, we introduce a physical quantity, shared purity, for arbitrary pure or mixed quantum states of shared systems of an arbitrary number of parties in arbitrary dimensions. We find that it is different from quantum correlations. However, we prove that a maximal shared purity between two parties excludes any shared purity of these parties with a third party, thus ensuring its quantum nature. Moreover, we show that all generalized GHZ states are monogamous, while all generalized W states are non-monogamous with respect to this measure. We apply the quantity to investigate the quantum XY spin models, and observe that it can faithfully detect the quantum phase transition present in these models. We perform a finite-size scaling analysis and find the scaling exponent for this quantity.

quant-ph↗

arXiv2014

Solution for an interaction quench in the Lieb-Liniger Bose gas

We study a quench protocol where the ground state of a free many-particle bosonic theory in one dimension is let unitarily evolve in time under the integrable Lieb-Liniger Hamiltonian of $δ$-interacting repulsive bosons. By using a recently-proposed variational method, we here obtain the exact non-thermal steady-state of the system in the thermodynamic limit, and discuss some of its main physical properties. Besides being a rare case of a thermodynamically exact solution to a truly interacting quench situation, this interestingly represents an example where a naive implementation of the generalized Gibbs ensemble fails.

cond-mat.stat-mech↗

arXiv2014

Lee-Yang cluster expansion approach to the BCS-BEC crossover: BCS and BEC limits

It is shown that a cluster expansion technique, which is usually applied in the high-temperature regime to calcutate virial coefficients, can be applied to evaluate the superfluid transition temperature of the BCS-BEC crossover à la Lee and Yang. The transition temperature is identified with the emergence of the singularity in the sum of a certain infinite series of cluster functions. In the weak-coupling limit, we reproduce the Thouless criterion and the number equation of Nozières and Schmitt-Rink, and hence the transition temperature of the BCS theory. In the strong-coupling limit, we reproduce the transition temperature of Bose-Einstein condensation of non-interacting tightly bound dimers.

cond-mat.quant-gas↗

arXiv2014

Locality and thermalization in closed quantum systems

We derive a necessary and sufficient condition for the thermalization of a local observable in a closed quantum system which offers an alternative explanation, independent of the eigenstate thermalization hypothesis, for the thermalization process. We also show that this approach is useful to investigate thermalization based on a finite-size scaling of numerical data. The condition follows from an exact representation of the observable as a sum of a projection onto the local conserved charges of the system and a projection onto the non-local ones. We show that thermalization requires that the time average of the latter part vanishes in the thermodynamic limit while time and statistical averages for the first part are identical. As an example, we use this thermalization condition to analyze exact diagonalization data for a one-dimensional spin model. We find that local correlators do thermalize in the thermodynamic limit although we find no indications that the eigenstate thermalization hypothesis applies.

cond-mat.stat-mech↗

arXiv2014

Superfluid-Mott insulator transition in spin-orbit coupled Bose-Hubbard Model

We consider a square optical lattice in two dimensions and study the effects of both the strength and symmetry of spin-orbit-coupling (SOC) and Zeeman field on the ground-state, i.e., Mott insulator (MI) and superfluid (SF), phases and phase diagram, i.e., MI-SF phase transition boundary, of the two-component Bose-Hubbard model. In particular, based on a variational Gutzwiller ansatz, our numerical calculations show that the spin-orbit coupled SF phase is a nonuniform (twisted) one with its phase (but not the magnitude) of the order parameter modulating from site to site. Fully analytical insights into the numerical results are also given.

cond-mat.quant-gas↗

arXiv2014

Ferromagnetism in a two-component Bose-Hubbard model with a synthetic spin-orbit coupling

We study the effect of the synthetic spin-orbit coupling in a two-component Bose-Hubbard model in one dimension by employing the density-matrix renormalization group method. A ferromagnetic long-range order emerges in both Mott insulator and superfluid phases resulting from the spontaneous breaking of the $Z_2$ symmetry, when the spin-orbit coupling term becomes comparable to the hopping kinetic energy and the inter-component interaction is smaller than the intra-one as well. This novel effect is expected to be detectable with the present realization of the synthetic spin-orbit coupling in experiments.

cond-mat.str-el↗

arXiv2014

Scaling of Entanglement Entropy in Point Contact Free Fermion Systems

The scaling of entanglement entropy is computationally studied in several $1\le d \le 2$ dimensional free fermion systems that are connected by one or more point contacts (PC). For both the $k$-leg Bethe lattice $(d =1)$ and $d=2$ rectangular lattices with a subsystem of $L^d$ sites, the entanglement entropy associated with a {\sl single} PC is found to be generically $S \sim L$. We argue that the $O(L)$ entropy is an expression of the subdominant $O(L)$ entropy of the bulk entropy-area law. For $d=2$ (square) lattices connected by $m$ PCs, the area law is found to be $S \sim aL^{d-1} + b m \log{L}$ and is thus consistent with the anomalous area law for free fermions ($S \sim L \log{L}$) as $m \rightarrow L$. For the Bethe lattice, the relevance of this result to Density Matrix Renormalization Group (DMRG) schemes for interacting fermions is discussed.

cond-mat.str-el↗

arXiv2013

Inhomogeneous BCS-BEC crossover for trapped cold atoms in optical lattices

The BCS-BEC crossover in a lattice is a powerful paradigm to understand how a superconductor deviates from the Bardeen-Cooper-Schrieffer physics as the attractive interaction increases. Optical lattices loaded with binary mixtures of cold atoms allow to address it experimentally in a clean and controlled way. We show that, however, the possibility to study this phenomenon in actual cold-atoms experiments is limited by the effect of the trapping potential. Real-space Dynamical Mean-Field Theory calculations show indeed that interactions and the confining potential conspire to pack the fermions in the center of the trap, which approaches a band insulator when the attraction become sizeable. We show how this physics reflects in several observables, and we propose an alternative strategy to disentangle the effect of the harmonic potential and measure the intrinsic properties resulting from the interaction strength.

cond-mat.str-el↗

arXiv2011

Multistage Kondo effect as a manifestation of dynamical symmetries in the single- and two-electron tunneling

The concept of dynamical symmetries is used for formulation of the renormalization group approach to the Kondo effect in the Anderson model with repulsive and attractive interaction $U$. It is shown that the generic local symmetry of the Anderson Hamiltonian is determined by the SU(4) Lie group. The Anderson Hamiltonian is rewritten in terms of the Gell-Mann matrices of the 4-th rank, which form the set of group generators and the basis for construction of irreducible vector operators describing the excitation spectra in the charge and spin sectors. The multistage Kondo sceening is described in terms of the local SU(4) dynamical symmetry. It is shown that the similarity between the conventional Kondo cotunneling effect for spin 1/2 in the positive $U$ model and the Kondo resonance for pair tunneling in the negative $U$ model is a direct manifestation of implicit SU(4) symmetry of the Anderson/Kondo model.

cond-mat.str-el↗

arXiv2021

Magnetic anisotropy in uranium monosulfide, probed by the magnetic torque measurements

We have studied the magnetic torque in uranium monosulfide (US) single crystals to explore the magnetic anisotropy in this material. Uranium monosulfide crystallizes in cubic, NaCl-type of crystal structure and exhibits the largest magneto-crystalline anisotropy observed in cubic systems. By performing detailed torque measurements we observe a strongly anisotropic behavior in the paramagnetic phase due to crystal defects and quadrupolar pair interactions. Our studies also confirm the presence of a large anisotropy in the ferromagnetic state of the US system with the <100>, <111>, and <110> directions being hard, easy, and intermediate axis, respectively. Furthermore, the anisotropy in the paramagnetic phase shows similar characteristics to the anisotropy observed in the ferromagnetic phase, as characterized by second and fourth rank susceptibility terms. The similarity of the anisotropic behaviors in paramagnetic and ferromagnetic phases is the consequence of strong magneto-elastic properties in this system, which possibly lead to the rhombohedral structural distortion, not only in the ferromagnetic phase but also in the paramagnetic phase (induced by applied magnetic fiield).

cond-mat.str-el↗