arXiv subjects

M. A. Cazalilla

Publications and source records attributed to M. A. Cazalilla.

At least 19 recordsLinked to original sources

arXiv2026

Superconducting Spin-Singlet QuBit in a Triangulene Spin Chain

Chains of triangular nanographene (triangulene), recently identified as realizing the valence-bond solid phase of a spin-1 chain, offer a promising platform for quantum information processing. We propose a spin-singlet qubit based on these chains grown on a superconducting substrate. Using the numerical renormalization group (NRG), we identify a manifold consisting of the two lowest-lying, spin-singlet states isolated from doublet states of opposite fermion parity, which undergo an avoided crossing. A qubit utilizing these states is thus protected from random Zeeman and/or spin-orbit coupling. Despite the unavoidable effect of quasiparticle poisoning on qubit performance, the isolation of the singlet states offers additional protection. In addition, we introduce a mesoscopic device architecture, based on a triple quantum dot coupled to a superconducting junction, that quantum simulates the spin chain and enables control and readout of the qubit. An effective two-level description of the device is validated using time-dependent NRG.

cond-mat.mes-hall↗

arXiv2024

Competition of Exchange and Correlation Energies in Two-Dimensional $N$-component Electron Gas Ferromagnetism

Motivated by recent observations of symmtry broken phases in lightly-doped multilayer graphene, we investigate magnetic phase transitions in a generalized electron gas model with four-component electron spin. This model simplifies the problem with a parabolic dispersion band, abstracting away the details of the graphene band structure to focus solely on the effects of the Coulomb interaction. We report four findings: 1) In the Hartree-Fock approximation, we observe that the paramagnetic state undergoes a sequence of density-driven, first-order phase transitions, progressively depopulating electrons from each spin component until achieving complete polarization within a very narrow density window where $1.2<r_s<2$ ($r_s$ being the electron gas parameter). 2) Further incorporating the correlation energy via the Bohm-Pines random-phase approximation shows that the cascade of transitions obtained within Hartree-Fock approximation is replaced by a single ferromagnetic phase transition at $r_s = 6.12$. 3) The disappearance of cascade is due to the correlation energy difference between the four-component paramagnetic state and symmetry-broken phases, which is nearly an order of magnitude more negative than the corresponding Hartree-Fock energy difference for $1.2 < r_s < 2$. 4) The transition from the paramagnetic state to the fully polarized state at $r_s=6.12$ is governed by the balance between exchange and correlation energies, a competition that cannot be captured by mean-field approximations to models featuring effective (density-dependent) delta-function interactions, such as the Stoner model. We use the insights from our model to comment on the phase diagram of multilayer graphene electron gas.

cond-mat.str-el↗

arXiv2023

Robust Spin Polarization of Yu-Shiba-Rusinov States in Superconductor/Ferromagnetic Insulator Heterostructures

Yu-Shiba-Rusinov (YSR) states arise as sub-gap excitations of a magnetic impurity in a superconducting host. Taking into account the quantum nature of the impurity spin in a single-site approximation, we study the spectral properties of the YSR excitations of a system of magnetic impurity in a spin-split superconductor, i.e. a superconductor in proximity to a ferromagnetic insulator at zero external magnetic fields. The YSR excitations of this system exhibit a robust spin-polarization that is protected from fluctuations and environmental noise by the exchange field of the ferromagnetic insulator, which can be as large as a few Tesla. We compare the results of this quantum approach to the classical approach, which conventionally predicts fully polarized YSR excitations even in the absence of exchange and external magnetic field. Turning on a small magnetic field, we show the latter splits the YSR excitations in the regime where the impurity is strongly coupled to the superconductor, whilst the classical approach predicts no such splitting. The studied system can potentially be realized in a tunnel junction connected to a quantum dot in proximity to a spin-split superconductor.

cond-mat.supr-con↗

arXiv2016

Quantum Quenches in the Luttinger model and its close relatives

A number of results on quantum quenches in the Luttinger and related models are surveyed with emphasis on post-quench correlations. For the Luttinger model and initial gaussian states, we discuss both sudden and smooth quenches of the interaction and the emergence of a steady state described by a generalized Gibbs ensemble. Comparisons between analytics and numerics, and the question of universality or lack thereof are also discussed. The relevance of the theoretical results to current and future experiments in the fields of ultracold atomic gases and mesoscopic systems of electrons is also briefly touched upon. Wherever possible, our approach is pedagogical and self-contained. This work is dedicated to the memory of our colleague Alejandro Muramatsu.

cond-mat.stat-mech↗

arXiv2014

Ultracold Fermi Gases with Emergent SU(N) Symmetry

We review recent experimental and theoretical progress on ultracold alkaline-earth Fermi gases with emergent SU$(N)$ symmetry. Emphasis is placed on describing the ground-breaking experimental achievements of recent years. The latter include the cooling to below quantum degeneracy of various isotopes of ytterbium and strontium, the demonstration of optical Feshbach resonances and the optical Stern-Gerlach effect, the realization of a Mott insulator of $^{173}$Yb atoms, the creation of various kinds of Fermi-Bose mixtures and the observation of many-body physics in optical lattice clocks. On the theory side, we survey the zoo of phases that have been predicted for both gases in a trap and loaded into an optical lattice, focusing on two and three-dimensional systems. We also discuss some of the challenges that lie ahead for the realization of such phases, such as reaching the temperature scale required to observe magnetic and more exotic quantum orders, and dealing with collisional relaxation of excited electronic levels.

cond-mat.quant-gas↗

arXiv2014

Extrinsic spin Hall effect induced by resonant skew scattering in graphene

We show that the extrinsic spin Hall effect can be engineered in monolayer graphene by decoration with small doses of adatoms, molecules, or nanoparticles originating local spin-orbit perturbations. The analysis of the single impurity scattering problem shows that intrinsic and Rashba spin-orbit local couplings enhance the spin Hall effect via skew scattering of charge carriers in the resonant regime. The solution of the transport equations for a random ensemble of spin-orbit impurities reveals that giant spin Hall currents are within the reach of the current state of the art in device fabrication. The spin Hall effect is robust with respect to thermal fluctuations and disorder averaging.

cond-mat.mes-hall↗

arXiv2014

Quantum Quench and Prethermalization Dynamics in A Two-Dimensional Fermi Gas with Long-range Interactions

We study the effect of suddenly turning on a long-range interaction in a spinless Fermi gas in two dimensions. The short to intermediate time dynamics is obtained using the method of bosonization of the Fermi surface. This allow to calculate the full space-time dependence of the non-equilibrium fermion density matrix as well as the evolution of the quasiparticle residue after the quench. It is thus found that the asymptotic state predicted by bosonization is consistent with the prethermalized state. From the bosonized representation, we explicitly construct the Generalized Gibbs Ensamble that describes the prethermalized state. A protocol to perform an interaction quantum quench in a dipolar gas of Erbium atoms is also described.

cond-mat.quant-gas↗

arXiv2013

Quantum Spin Hall Effect in Two-dimensional Crystals of Transition Metal Dichalcogenides

We propose to engineer time-reversal-invariant topological insulators in two-dimensional (2D) crystals of transition metal dichalcogenides (TMDCs). We note that, at low doping, semiconducting TMDCs under shear strain will develop spin-polarized Landau levels residing in different valleys. We argue that gaps between Landau levels in the range of $10-100$ Kelvin are within experimental reach. In addition, we point out that a superlattice arising from a Moiré pattern can lead to topologically non-trivial subbands. As a result, the edge transport becomes quantized, which can be probed in multi-terminal devices made using strained 2D crystals and/or heterostructures. The strong $d$ character of valence and conduction bands may also allow for the investigation of the effects of electron correlations on the topological phases.

cond-mat.mes-hall↗

arXiv2013

Dissipative Effects on the Superfluid to Insulator Transition in Mixed-dimensional Optical Lattices

We study the superfluid to Mott insulator transition of a mixture of heavy bosons and light fermions loaded in an optical lattice. We focus on the effect of the light fermions on the dynamics of the heavy bosons. It is shown that, when the lattice potential is sufficiently deep to confine the bosons to one dimension but allowing the fermions to freely move in three dimensions (i.e. a mixed-dimensionality lattice), the fermions act as an ohmic bath for bosons leading to screening and dissipation effects on the bosons. Using a perturbative renormalization-group analysis, it is shown that the fermion-induced dissipative effects have no appreciable impact on the transition from the superfluid to the Mott-insulator state at integer filling. On the other hand, dissipative effects are found to be very important in the half-filled case near the critical point. In this case, in the presence of a finite incommensurability that destabilizes the Mott phase, the bosons can still be localized by virtue of dissipative effects.

cond-mat.quant-gas↗

arXiv2013

Phase Equilibrium of Binary Mixtures in Mixed Dimensions

We study the stability of a Bose-Fermi system loaded into an array of coupled one-dimensional (1D) "tubes", where bosons and fermions experience different dimensions: Bosons are heavy and strongly localized in the 1D tubes, whereas fermions are light and can hop between the tubes. Using the 174Yb-6Li system as a reference, we obtain the equilibrium phase diagram. We find that, for both attractive and repulsive interspecies interaction, the exact treatment of 1D bosons via the Bethe ansatz implies that the transitions between pure fermion and any phase with a finite density of bosons can only be first order and never continuous, resulting in phase separation in density space. In contrast, the order of the transition between the pure boson and the mixed phase can either be second or first order depending on whether fermions are allowed to hop between the tubes or they also are strictly confined in 1D. We discuss the implications of our findings for current experiments on 174Yb-6Li mixtures as well as Fermi-Fermi mixtures of light and heavy atoms in a mixed dimensional optical lattice system.

cond-mat.quant-gas↗

arXiv2012

Local Moment Formation and Kondo Effect in Defective Graphene

We study the local moment formation and the Kondo effect at single-atom vacancies in Graphene. We develop a model accounting for the vacancy reconstruction as well as non-planarity effects induced by strain and/or temperature. Thus, we find that the dangling $σ$ orbital localized at the vacancy is allowed to strongly hybridize with the $π$-band since the scattering with the vacancy turns the hybridization into singular function of the energy ($\sim [|ε| \ln^2 ε/D]^{-1}$, $D\sim$ the bandwidth). This leads to several new types of impurity phases, which control the magnitude of the vacancy magnetic moment and the possibility of Kondo effect depending on the strength of the local Coulomb interactions, the Hund's rule coupling, the doping level, and the degree of particle-symmetry breaking.

cond-mat.str-el↗

arXiv2011

One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases

We review the physics of one-dimensional interacting bosonic systems. Beginning with results from exactly solvable models and computational approaches, we introduce the concept of bosonic Tomonaga-Luttinger Liquids relevant for one-dimension, and compare it with Bose-Einstein condensates existing in dimensions higher than one. We discuss the effects of various perturbations on the Tomonaga-Luttinger liquid state as well as extensions to multicomponent and out of equilibrium situations. Finally, we review the experimental systems that can be described in terms of models of interacting bosons in one dimension.

cond-mat.str-el↗

arXiv2010

A Composite Fermion Approach to the Ultracold Dilute Fermi Gas

It is argued that the recently observed Fermi liquids in strongly interacting ultracold Fermi gases are adiabatically connected to a projected Fermi gas. This conclusion is reached by constructing a set of Jastrow wavefunctions, following Tan's observations on the structure of the physical Hilbert space [Annals of Physics 323, 2952 (2008)]. The Jastrow projection merely implements the Bethe-Peierls condition on the BCS and Fermi gas wavefunctions. This procedure provides a simple picture of the emergence of Fermi polarons as composite fermions in the normal state of the highly polarized gas. It is also shown that the projected BCS wavefunction can be written as a condensate of pairs of composite fermions (or Fermi polarons). A Hamiltonian for the composite fermions is derived. Within a mean-field theory, it is shown that the ground state and excitations of this Hamiltonian are those of a non-interacting Fermi gas although they are described by Jastrow-Slater wavefunctions.

cond-mat.quant-gas↗

arXiv2010

Quantum quench dynamics of the sine-Gordon model in some solvable limits

In connection with the the thermalization problem in isolated quantum systems, we investigate the dynamics following a quantum quench of the sine-Gordon model in the Luther-Emery and the semiclassical limits. We consider the quench from the gapped to the gapless phase as well as reversed one. By obtaining analytic expressions for the one and two-point correlation functions of the order parameter operator at zero-temperature, the manifestations of integrability in the absence of thermalization in the sine-Gordon model are studied. It is thus shown that correlations in the long time regime after the quench are well described by a generalized Gibbs ensemble. We also consider the case where the system is initially in contact with a reservoir at finite temperature. The possible relevance of our results to current and future experiments with ultracold atomic systems is also critically considered.

cond-mat.quant-gas↗

arXiv2009

Lattice modulation spectroscopy of strongly interacting bosons in disordered and quasi-periodic optical lattices

We compute the absorption spectrum of strongly repulsive one-dimensional bosons in a disordered or quasi-periodic optical lattice. At commensurate filling, the particle-hole resonances of the Mott insulator are broadened as the disorder strength is increased. In the non-commensurate case, mapping the problem to the Anderson model allows us to study the Bose-glass phase. Surprisingly we find that a perturbative treatment in both cases, weak and strong disorder, gives a good description at all frequencies. In particular we find that the infrared absorption rate in the thermodynamic limit is quadratic in frequency. This result is unexpected, since for other quantities like the conductivity in one dimensional systems, perturbation theory is only applicable at high frequencies. We discuss applications to recent experiments on optical lattice systems, and in particular the effect of the harmonic trap.

cond-mat.quant-gas↗

arXiv2009

Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System

It is argued that ultracold quantum degenerate gas of ytterbium $^{173}$Yb atoms having nuclear spin $I = 5/2$ exhibits an enlarged SU$(6)$ symmetry. Within the Landau Fermi liquid theory, stability criteria against Fermi liquid (Pomeranchuk) instabilities in the spin channel are considered. Focusing on the SU$(n > 2)$ generalizations of ferromagnetism, it is shown within mean-field theory that the transition from the paramagnet to the itinerant ferromagnet is generically first order. On symmetry grounds, general SU$(n)$ itinerant ferromagnetic ground states and their topological excitations are also discussed. These SU$(n > 2)$ ferromagnets can become stable by increasing the scattering length using optical methods or in an optical lattice. However, in an optical lattice at current experimental temperatures, Mott states with different filling are expected to coexist in the same trap, as obtained from a calculation based on the SU$(6)$ Hubbard model.

cond-mat.quant-gas↗

arXiv2009

Quantum quench dynamics of some exactly solvable models in one dimension

The dynamics of the Luttinger model and the sine-Gordon model (at the Luther-Emery point and in the semiclassical approximation) after a quantum quench is studied. We compute in detail one and two-point correlation functions for different types of quenches: from a non-interacting to an interacting Luttinger model and vice-versa, and from the gapped to the gapless phase of the sine-Gordon model and vice-versa. A progressive destruction of the Fermi gas features in the momentum distribution is found in the case of a quench into an interacting state in the Luttinger model. The critical exponents for spatial correlations are also found to be different from their equilibrium values. Correlations following a quench of the sine-Gordon model from the gapped to the gapless phase are found in agreement with the predictions of Calabrese and Cardy [Phys. Rev. Lett. {\bf 96} 136801 (2006)]. However, correlations following a quench from the gapped to the gapless phase at the Luther-Emery and the semi-classical limit exhibit a somewhat different behavior, which may indicate a break-down of the semiclassical approximation or a qualitative change in the behavior of correlations as one moves away from the Luther-Emergy point. In all cases, we find that the correlations at infinite times after the quench are well described by a generalized Gibbs ensemble [M. Rigol \emph{et al.} Phys. Rev. Lett. {\bf 98}, 050405 (2007)], which assigns a momentum dependent temperature to each eigenmode.

cond-mat.str-el↗

arXiv2009

Quantum Simulation of the Hubbard Model: The Attractive Route

We study the conditions under which, using a canonical transformation, the phases sought after for the repulsive Hubbard model, namely a Mott insulator in the paramagnetic and anti-ferromagnetic phases, and a putative d-wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultra-cold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We show that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are in fact more easy to observe as a paired, and superfluid phase respectively, in the attractive Hubbard model. The putative d-wave superfluid phase of the repulsive Hubbard model doped away from half-filling is related to a d-wave antiferromagnetic phase for the attractive Hubbard model. We discuss the advantages of this approach to 'quantum simulate' the Hubbard model in an optical lattice over the approach that attempts to directly simulate the doped Hubbard model in the repulsive regime. We also point out a number of technical difficulties of the proposed approach and, in some cases, suggest possible solutions.

cond-mat.str-el↗