arXiv subjects

Sebastiano Peotta

Publications and source records attributed to Sebastiano Peotta.

33 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

Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models

In a partially filled flat Bloch band electrons do not have a well defined Fermi surface and hence the low-energy theory is not a Fermi liquid. Neverethless, under the influence of an attractive interaction, a superconductor well described by the Bardeen-Cooper-Schrieffer (BCS) wave function can arise. Here we study the low-energy effective Hamiltonian of a generic Hubbard model with a flat band. We obtain an effective Hamiltonian for the flat band physics by eliminating higher lying bands via perturbative Schrieffer-Wolff transformation. At first order in the interaction energy we recover the usual procedure of projecting the interaction term onto the flat band Wannier functions. We show that the BCS wave function is the exact ground state of the projected interaction Hamiltonian and that the compressibility is diverging as a consequence of an emergent $SU(2)$ symmetry. This symmetry is broken by second order interband transitions resulting in a finite compressibility, which we illustrate for a one-dimensional ladder with two perfectly flat bands. These results motivate a further approximation leading to an effective ferromagnetic Heisenberg model. The gauge-invariant result for the superfluid weight of a flat band can be obtained from the ferromagnetic Heisenberg model only if the maximally localized Wannier functions in the Marzari-Vanderbilt sense are used. Finally, we prove an important inequality $D \geq \mathcal{W}^2$ between the Drude weight $D$ and the winding number $\mathcal{W}$, which guarantees ballistic transport for topologically nontrivial flat bands in one dimension.

cond-mat.str-el↗

arXiv2016

Geometric origin of superfluidity in the Lieb lattice flat band

The ground state and transport properties of the Lieb lattice flat band in the presence of an attractive Hubbard interaction are considered. It is shown that the superfluid weight can be large even for an isolated and strictly flat band. Moreover the superfluid weight is proportional to the interaction strength and to the quantum metric, a band structure invariant obtained from the flat-band Bloch functions. These predictions are amenable to verification with ultracold gases and may explain the anomalous behaviour of the superfluid weight of high-Tc superconductors.

cond-mat.quant-gas↗

arXiv2015

Superfluidity in topologically nontrivial flat bands

Topological invariants built from the periodic Bloch functions characterize new phases of matter, such as topological insulators and topological superconductors. The most important topological invariant is the Chern number that explains the quantized conductance of the quantum Hall effect. Here, we provide a general result for the superfluid weight $D_{\rm s}$ of a multiband superconductor that is applicable to topologically nontrivial bands with nonzero Chern number $C$. We find that the integral over the Brillouin zone of the quantum metric, an invariant calculated from the Bloch functions, gives the superfluid weight in a flat band, with the bound $D_{\rm s} \geq |C|$. Thus, even a flat band can carry finite superfluid current, provided the Chern number is nonzero. As an example, we provide $D_{\rm s}$ for the time-reversal invariant attractive Harper-Hubbard model that can be experimentally tested in ultracold gases. In general, our results establish that a topologically nontrivial flat band is a promising concept for increasing the critical temperature of the superconducting transition.

cond-mat.supr-con↗

arXiv2015

Dynamical symmetry and pair tunneling in a one-dimensional Bose gas colliding with a mobile impurity

Using the time-dependent density matrix renormalization group (TDMRG) we theoretically study the collision of a one-dimensional gas of interacting bosons with an impurity trapped in a shallow box potential. We study the dynamic response of both the impurity and the bosonic gas and find an approximate independence of the sign of the interaction (attractive or repulsive) between the impurity and the bosons. This sign-independence breaks down when the interaction energy is of the same order as the box potential depth, leading to resonant pair tunneling. Our predictions can be tested using contemporary techniques with ultracold atoms.

cond-mat.quant-gas↗

arXiv2015

Quantum transport in ultracold atoms

Ultracold atoms confined by engineered magnetic or optical potentials are ideal systems for studying phenomena otherwise difficult to realize or probe in the solid state because their atomic interaction strength, number of species, density, and geometry can be independently controlled. This review focuses on quantum transport phenomena in atomic gases that mirror and oftentimes either better elucidate or show fundamental differences with those observed in mesoscopic and nanoscopic systems. We discuss significant progress in performing transport experiments in atomic gases, contrast similarities and differences between transport in cold atoms and in condensed matter systems, and survey inspiring theoretical predictions that are difficult to verify in conventional setups. These results further demonstrate the versatility offered by atomic systems in the study of nonequilibrium phenomena and their promise for novel applications.

cond-mat.quant-gas↗

arXiv2015

Edge binding of sine-Gordon solitons in spin-orbit coupled Bose-Einstein condensates

In recent experiments with ultracold gases a Raman coupling scheme is used to produce both spin-orbit (SO) and Zeeman-type couplings [Y.-J. Lin et al., Nature 471, 83 (2011)]. Their competition drives a phase transition to a magnetized state with broken $Z_2$ symmetry. Using a hydrodynamic approach we study a confined binary condensate subject to both SO and Zeeman-type couplings. We find that in the limit of small healing length and in the phase with unbroken symmetry, the boundary magnetization profile has an analytical solution in the form of a sine-Gordon soliton. The soliton is bound to the edge of the system by the nontrivial boundary condition resulting from the combined effect of the SO coupling and the drop in the particle density. The same boundary condition is important in the magnetized phase as well, where we characterize numerically the boundary spin structure. We further discuss how the nontrivial magnetization structure affects the density profile near the boundary, yet another prediction that can be tested in current experiments of spin-orbit coupled condensates.

cond-mat.quant-gas↗

arXiv2014

Phase-induced transport in atomic gases: from superfluid to Mott insulator

Recent experimental realizations of artificial gauge fields for cold atoms are promising for generating steady states carrying a mass current in strongly correlated systems, such as the Bose-Hubbard model. Moreover, a homogeneous condensate confined by hard-wall potentials from laser sheets has been demonstrated, which provides opportunities for probing the intrinsic transport properties of isolated quantum systems. Using the time-dependent Density Matrix Renormalization Group (TDMRG), we analyze the effect of the lattice and interaction strength on the current generated by a quench in the artificial vector potential when the density varies from low values (continuum limit) up to integer filling in the Mott-insulator regime. There is no observable mass current deep in the Mott-insulator state as one may expect. Other observable quantities used to characterize the quasi-steady state in the bulk of the system are the Drude weight and entanglement entropy production rate. The latter in particular provides a striking signature of the superfluid-Mott insulator transition. Furthermore, an interesting property of the superfluid state is the formation of shock and rarefaction waves at the boundaries due to the hard-wall confining potentials. We provide results for the height and the speed of the shock front that propagates from the boundary toward the center of the lattice. Our results should be verifiable with current experimental capabilities.

cond-mat.quant-gas↗

arXiv2014

Superconducting Memristors

In his original work Josephson predicted that a phase-dependent conductance should be present in superconducting tunnel junctions, an effect difficult to detect, mainly because it is hard to single it out from the usual non-dissipative Josephson current. We propose a solution for this problem that consists in using different superconducting materials to realize the two junctions of a superconducting interferometer. According to the Ambegaokar-Baratoff relation the two junctions have different conductances if the critical currents are equal, thus the Josephson current can be suppressed by fixing the magnetic flux in the loop at half of a flux quantum without cancelling the phase-dependent conductance. Our proposal can be used to study the phase-dependent conductance, an effect present in principle in all superconducting weak links. From the standpoint of nonlinear circuit theory such a device is in fact an ideal memristor with possible applications to memories and neuromorphic computing in the framework of ultrafast and low energy consumption superconducting digital circuits.

cond-mat.supr-con↗

arXiv2014

The XYZ chain with Dzyaloshinsky-Moriya interactions: from spin-orbit-coupled lattice bosons to interacting Kitaev chains

Using the density-matrix renormalization-group algorithm (DMRG) and a finite-size scaling analysis, we study the properties of the one-dimensional completely-anisotropic spin-1/2 XYZ model with Dzyaloshinsky-Moriya (DM) interactions. The model shows a rich phase diagram: depending on the value of the coupling constants, the system can display different kinds of ferromagnetic order and Luttinger-liquid behavior. Transitions from ferromagnetic to Luttinger-liquid phases are first order. We thoroughly discuss the transition between different ferromagnetic phases, which, in the absence of DM interactions, belongs to the XX universality class. We provide evidence that the DM exchange term turns out to split this critical line into two separated Ising-like transitions and that in between a disordered phase may appear. Our study sheds light on the general problem of strongly-interacting spin-orbit-coupled bosonic gases trapped in an optical lattice and can be used to characterize the topological properties of superconducting nanowires in the presence of an imposed supercurrent and of interactions.

cond-mat.stat-mech↗

arXiv2014

Quantum Shock Waves and Population Inversion in Collisions of Ultracold Atomic Clouds

Using Time-Dependent Density Matrix Renormalization Group (TDMRG) we study the collision of one-dimensional atomic clouds confined in a harmonic trap and evolving with the Lieb-Liniger Hamiltonian. It is observed that the motion is essentially periodic with the clouds bouncing elastically, at least on the time scale of the first few oscillations that can be resolved with high accuracy. This is in agreement with the results of the "quantum Newton cradle" experiment of Kinoshita et al. [Nature 440, 900 (2006)]. We compare the results for the density profile against a hydrodynamic description, or generalized nonlinear Schrödinger equation, with the pressure term taken from the Bethe Ansatz solution of the Lieb-Liniger model. We find that hydrodynamics can describe the breathing mode of a harmonically trapped cloud for arbitrary long times while it breaks down almost immediately for the collision of two clouds due to the formation of shock waves (gradient catastrophe). In the case of the clouds' collision TDMRG alone allows to extract the oscillation period which is found to be measurably different from the breathing mode period. Concomitantly with the shock waves formation we observe a local energy distribution typical of population inversion, i.e., an effective negative temperature. Our results are an important step towards understanding the hydrodynamics of quantum many-body systems out of equilibrium and the role of integrability in their dynamics.

cond-mat.quant-gas↗

arXiv2013

Improving the Gutzwiller Ansatz with Matrix Product States

The Gutzwiller variational wavefunction (GVW) is commonly employed to capture correlation effects in condensed matter systems such as ferromagnets, ultracold bosonic gases, correlated superconductors, etc. By noticing that the grand-canonical and number-conserving Gutzwiller Ansätze are in fact the zero-order approximation of an expansion in the truncation parameter of a Matrix Product State (MPS), we argue that MPSs, and the algorithms used to operate on them, are not only flexible computational tools but also a unifying theoretical framework that can be used to generalize and improve on the GVW. In fact, we show that a number-conserving GVW is less efficient in capturing the ground state of a quantum system than a more general MPS which can be optimized with comparable computational resources. Moreover, we suggest a corrected time-dependent density matrix renormalization group algorithm that ensures the conservation of the expectation value of the number of particles when a GVW or a MPS are not explicitly number-conserving. The GVW dynamics obtained with our algorithm compares very well with the exact one in 1D. Most importantly, the algorithm works in any dimension for a GVW. We thus expect it to be of great value in the study of the dynamics of correlated quantum systems.

cond-mat.quant-gas↗

arXiv2012

Short-time Spin Dynamics in Strongly Correlated Few-fermion Systems

The non-equilibrium spin dynamics of a one-dimensional system of repulsively interacting fermions is studied by means of density-matrix renormalization-group simulations. We focus on the short-time decay of the oscillation amplitudes of the centers of mass of spin-up and spin-down fermions. Due to many-body effects, the decay is found to evolve from quadratic to linear in time, and eventually back to quadratic as the strength of the interaction increases. The characteristic rate of the decay increases linearly with the strength of repulsion in the weak-coupling regime, while it is inversely proportional to it in the strong-coupling regime. Our predictions can be tested in experiments on tunable ultra-cold few-fermion systems in one-dimensional traps.

cond-mat.str-el↗

arXiv2012

Quantum Breathing of an Impurity in a One-dimensional Bath of Interacting Bosons

By means of time-dependent density-matrix renormalization-group (TDMRG) we are able to follow the real-time dynamics of a single impurity embedded in a one-dimensional bath of interacting bosons. We focus on the impurity breathing mode, which is found to be well-described by a single oscillation frequency and a damping rate. If the impurity is very weakly coupled to the bath, a Luttinger-liquid description is valid and the impurity suffers an Abraham-Lorentz radiation-reaction friction. For a large portion of the explored parameter space, the TDMRG results fall well beyond the Luttinger-liquid paradigm.

cond-mat.quant-gas↗

arXiv2011

Josephson current in a four terminal superconductor - exciton condensate - superconductor system

We investigate the transport properties of a bilayer exciton condensate that is contacted by four superconducting leads. We focus on the equilibrium regime and investigate how the Josephson currents induced in the bilayer by phase biases applied to the superconducting electrodes are affected by the presence of an exciton condensate in the bulk of the system. As long as the distance between the superconducting electrodes is much larger than the exciton coherence length, the Josephson current depends only on the difference between the phase biases in the two layers. This result holds true in both short- and long-junction limits. We relate it to a novel correlated four-particle Andreev process which occurs at the superconductor - exciton condensate interface. The system we investigate provides an implementation of the supercurrent mirror proposed by Kitaev as a viable way to realize topologically protected qubits.

cond-mat.supr-con↗