arXiv subjects

Marcello Dalmonte

Publications and source records attributed to Marcello Dalmonte.

At least 91 records · Page 5Linked to original sources

arXiv2018

Floquet time crystals in clock models

We construct a class of period-$n$-tupling discrete time crystals based on $\mathbb{Z}_n$ clock variables, for all the integers $n$. We consider two classes of systems where this phenomenology occurs, disordered models with short-range interactions and fully connected models. In the case of short-range models we provide a complete classification of time-crystal phases for generic $n$. For the specific cases of $n=3$ and $n=4$ we study in details the dynamics by means of exact diagonalisation. In both cases, through an extensive analysis of the Floquet spectrum, we are able to fully map the phase diagram. In the case of infinite-range models, the mapping onto an effective bosonic Hamiltonian allows us to investigate the scaling to the thermodynamic limit. After a general discussion of the problem, we focus on $n=3$ and $n=4$, representative examples of the generic behaviour. Remarkably, for $n=4$ we find clear evidence of a new crystal-to-crystal transition between period $n$-tupling and period $n/2$-tupling.

cond-mat.quant-gas↗

arXiv2018

Non-topological parafermions in a one-dimensional fermionic model with even multiplet pairing

We discuss a one-dimensional fermionic model with a generalized $\mathbb{Z}_{N}$ even multiplet pairing extending Kitaev $\mathbb{Z}_{2}$ chain. The system shares many features with models believed to host localized edge parafermions, the most prominent being a similar bosonized Hamiltonian and a $\mathbb{Z}_{N}$ symmetry enforcing an $N$-fold degenerate ground state robust to certain disorder. Interestingly, we show that the system supports a pair of parafermions but they are non-local instead of being boundary operators. As a result, the degeneracy of the ground state is only partly topological and coexists with spontaneous symmetry breaking by a (two-particle) pairing field. Each symmetry-breaking sector is shown to possess a pair of Majorana edge modes encoding the topological twofold degeneracy. Surrounded by two band insulators, the model exhibits for $N=4$ the dual of an $8 π$ fractional Josephson effect highlighting the presence of parafermions.

cond-mat.str-el↗

arXiv2018

String tension and robustness of confinement properties of in the Schwinger-Thirring model

Confinement properties of the $1+1$ Schwinger model can bestudied by computing the string tension between two charges. It is finite (vanishing) if the fermions are massive (massless) corresponding to the occurrence of confinement (screening). Motivated by the possibility of experimentally simulate the Schwinger model, we investigate here the robustness of its screened and confined phases. Firstly, we analyze the effect of nearest-neighbour density-density interaction terms, which -- in the absence of the gauge fields -- give rise to the Thirring model. The resulting Schwinger-Thirring model is studied, also in presence of a topological $θ$ term, showing that the massless (massive) model remains screened (confined) and that there is deconfinement only for $θ=\pmπ$ in the massive case. Estimates of the parameters of the Schwinger-Thirring model are provided with a discussion of a possible experimental setup for its realization with ultracold atoms. The possibility that the gauge fields live in higher dimensions while the fermions remain in $1+1$ is also considered. One may refer to this model as the Pseudo-Schwinger-Thirring model. It is shown that the screening of external charges occurs for $2+1$ and $3+1$ gauge fields, exactly as it occurs in $1+1$ dimensions, with a radical change of the long distance interaction induced by the gauge fields. The massive (massless) model continues to exhibit confinement (screening), signalling that it is the dimensionality of the matter fields, and not of the gauge fields to determine confinement properties. A computation for the string tension is presented in perturbation theory. Our conclusion is that $1+1$ models exhibiting confinement or screening -- massless or massive, in presence of a topological term or not -- retain their main properties when the Thirring interaction is added or the gauge fields live in higher dimension.

hep-th↗

arXiv2018

Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models

We present a scheme for measuring Rényi entropies in generic atomic Hubbard and spin models using single copies of a quantum state and for partitions in arbitrary spatial dimension. Our approach is based on the generation of random unitaries from random quenches, implemented using engineered time-dependent disorder potentials, and standard projective measurements, as realized by quantum gas microscopes. By analyzing the properties of the generated unitaries and the role of statistical errors, with respect to the size of the partition, we show that the protocol can be realized in exisiting AMO quantum simulators, and used to measure for instance area law scaling of entanglement in two-dimensional spin models or the entanglement growth in many-body localized systems.

quant-ph↗

arXiv2017

Many-body localization dynamics from gauge invariance

We show how lattice gauge theories can display many-body localization dynamics in the absence of disorder. Our starting point is the observation that, for some generic translationally invariant states, Gauss law effectively induces a dynamics which can be described as a disorder average over gauge super-selection sectors. We carry out extensive exact simulations on the real-time dynamics of a lattice Schwinger model, describing the coupling between U(1) gauge fields and staggered fermions. Our results show how memory effects and slow entanglement growth are present in a broad regime of parameters - in particular, for sufficiently large interactions. These findings are immediately relevant to cold atoms and trapped ions experiments realizing dynamical gauge fields, and suggest a new and universal link between confinement and entanglement dynamics in the many-body localized phase of lattice models.

cond-mat.str-el↗

arXiv2017

Fractional quantum Hall effect in the interacting Hofstadter model via tensor networks

We show via tensor network methods that the Harper-Hofstadter Hamiltonian for hard-core bosons on a square geometry supports a topological phase realizing the $ν=1/2$ fractional quantum Hall effect on the lattice. We address the robustness of the ground state degeneracy and of the energy gap, measure the many-body Chern number, and characterize the system using Green functions, showing that they decay algebraically at the edges of open geometries, indicating the presence of gapless edge modes. Moreover, we estimate the topological entanglement entropy by taking a combination of lattice bipartitions that reproduces the topological structure of the original proposals by Kitaev and Preskill, and Levin and Wen. The numerical results show that the topological contribution is compatible with the expected value $γ= 1/2$. Our results provide extensive evidence that FQH states are within reach of state-of-the-art cold atom experiments.

cond-mat.quant-gas↗

arXiv2017

Long-range interactions from $U\left(1\right)$ gauge fields via dimensional mismatch

We show how certain long-range models of interacting fermions in $d+1$ dimensions are equivalent to $U\left(1\right)$ gauge theories in $D+1$ dimensions, with the dimension $D$ in which gauge fields are defined larger than the dimension $d$ of the fermionic theory to be simulated. For $d=1$ it is possible to obtain an exact mapping, providing an expression of the fermionic interaction potential in terms of half-integer powers of the Laplacian. An analogous mapping can be applied to the kinetic term of the bosonized theory. A diagrammatic representation of the theories obtained by dimensional mismatch is presented, and consequences and applications of the established duality are discussed. Finally, by using a perturbative approach, we address the canonical quantization of fermionic theories presenting non-locality in the interaction term to construct the Hamiltonians for the effective theories found by dimensional reduction. We conclude by showing that one can engineer the gauge fields and the dimensional mismatch in order to obtain long-range effective Hamiltonians with $1/r$ potentials.

cond-mat.stat-mech↗

arXiv2017

Quantum Simulation and Spectroscopy of Entanglement Hamiltonians

Entanglement is central to our understanding of many-body quantum matter. In particular, the entanglement spectrum, as eigenvalues of the reduced density matrix of a subsystem, provides a unique footprint of properties of strongly correlated quantum matter from detection of topological order to characterisation of quantum critical systems. However, direct experimental measurement of the entanglement spectrum has so far remained elusive due to lack of direct experimental probes. Here we show that the entanglement spectrum of the ground state of a broad class of Hamiltonians becomes directly accessible as quantum simulation and spectroscopy of an entanglement Hamil- tonian, building on the Bisognano-Wichmann (BW) theorem of axiomatic quantum field theory. Remarkably, this theorem gives an explicit physical construction of the entanglement Hamiltonian, identified as Hamiltonian of the many-body system of interest with spatially varying couplings. Building on this, we propose an immediate, scalable recipe for implementation of the entanglement Hamiltonian, and measurement of the corresponding entanglement spectrum as spectroscopy of the Bisognano-Wichmann Hamiltonian with synthetic quantum systems, including atoms in optical lat- tices and trapped ions. We illustrate and benchmark this scenario on a variety of models, spanning phenomena as diverse as conformal field theories, topological order, and quantum phase transitions.

cond-mat.str-el↗

arXiv2017

Floquet time crystal in the Lipkin-Meshkov-Glick model

In this work we discuss the existence of time-translation symmetry breaking in a kicked infinite-range-interacting clean spin system described by the Lipkin-Meshkov-Glick model. This Floquet time crystal is robust under perturbations of the kicking protocol, its existence being intimately linked to the underlying $\mathbb{Z}_2$ symmetry breaking of the time-independent model. We show that the model being infinite-range and having an extensive amount of symmetry breaking eigenstates is essential for having the time-crystal behaviour. In particular we discuss the properties of the Floquet spectrum, and show the existence of doublets of Floquet states which are respectively even and odd superposition of symmetry broken states and have quasi-energies differing of half the driving frequencies, a key essence of Floquet time crystals. Remarkably, the stability of the time-crystal phase can be directly analysed in the limit of infinite size, discussing the properties of the corresponding classical phase space. Through a detailed analysis of the robustness of the time crystal to various perturbations we are able to map the corresponding phase diagram. We finally discuss the possibility of an experimental implementation by means of trapped ions.

cond-mat.stat-mech↗

arXiv2017

Laughlin-like states in bosonic and fermionic atomic synthetic ladders

The combination of interactions and static gauge fields plays a pivotal role in our understanding of strongly-correlated quantum matter. Cold atomic gases endowed with a synthetic dimension are emerging as an ideal platform to experimentally address this interplay in quasi-one-dimensional systems. A fundamental question is whether these setups can give access to pristine two-dimensional phenomena, such as the fractional quantum Hall effect, and how. We show that unambiguous signatures of bosonic and fermionic Laughlin-like states can be observed and characterized in synthetic ladders. We theoretically diagnose these Laughlin-like states focusing on the chiral current flowing in the ladder, on the central charge of the low-energy theory, and on the properties of the entanglement entropy. Remarkably, Laughlin-like states are separated from conventional liquids by Lifschitz-type transitions, characterized by sharp discontinuities in the current profiles, which we address using extensive simulations based on matrix-product states. Our work provides a qualitative and quantitative guideline towards the observability and understanding of strongly-correlated states of matter in synthetic ladders. In particular, we unveil how state-of-the-art experimental settings constitute an ideal starting point to progressively tackle two-dimensional strongly interacting systems from a ladder viewpoint, opening a new perspective for the observation of non-Abelian states of matter.

cond-mat.quant-gas↗

arXiv2017

Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks

We investigate the finite-density phase diagram of a non-abelian SU(2) lattice gauge theory in (1+1)-dimensions using tensor network methods. We numerically characterise the phase diagram as a function of the matter filling and of the matter-field coupling, identifying different phases, some of them appearing only at finite densities. For weak matter-field coupling we find a meson BCS liquid phase, which is confirmed by second-order analytical perturbation theory. At unit filling and for strong coupling, the system undergoes a phase transition to a charge density wave of single-site (spin-0) mesons via spontaneous chiral symmetry breaking. At finite densities, the chiral symmetry is restored almost everywhere, and the meson BCS liquid becomes a simple liquid at strong couplings, with the exception of filling two-thirds, where a charge density wave of mesons spreading over neighbouring sites appears. Finally, we identify two tri-critical points between the chiral and the two liquid phases which are compatible with a $SU(2)_2$ Wess-Zumino-Novikov-Witten model. Here we do not perform the continuum limit but we explicitly address the global $U(1)$ charge conservation symmetry.

quant-ph↗

arXiv2017

Adiabatic state preparation of stripe phases with strongly magnetic atoms

We propose a protocol for realizing the stripe phase in two spin models on a two-dimensional square lattice, which can be implemented with strongly magnetic atoms (Cr, Dy, Er, etc.) in optical lattices by encoding spin states into Zeeman sublevels of the ground state manifold. The protocol is tested with cluster-mean-field time-dependent variational ansätze, validated by comparison with exact results for small systems, which enable us to simulate the dynamics of systems with up to 64 sites during the state-preparation protocol. This allows, in particular, to estimate the time required for preparation of the stripe phase with high fidelity under real experimental conditions.

cond-mat.quant-gas↗

arXiv2016

U(1) Wilson lattice gauge theories in digital quantum simulators

Lattice gauge theories describe fundamental phenomena in nature, but calculating their real-time dynamics on classical computers is notoriously difficult. In a recent publication [Nature 534, 516 (2016)], we proposed and experimentally demonstrated a digital quantum simulation of the paradigmatic Schwinger model, a U(1)-Wilson lattice gauge theory describing the interplay between fermionic matter and gauge bosons. Here, we provide a detailed theoretical analysis of the performance and the potential of this protocol. Our strategy is based on analytically integrating out the gauge bosons, which preserves exact gauge invariance but results in complicated long-range interactions between the matter fields. Trapped-ion platforms are naturally suited to implementing these interactions, allowing for an efficient quantum simulation of the model, with a number of gate operations that scales only polynomially with system size. Employing numerical simulations, we illustrate that relevant phenomena can be observed in larger experimental systems, using as an example the production of particle--antiparticle pairs after a quantum quench. We investigate theoretically the robustness of the scheme towards generic error sources, and show that near-future experiments can reach regimes where finite-size effects are insignificant. We also discuss the challenges in quantum simulating the continuum limit of the theory. Using our scheme, fundamental phenomena of lattice gauge theories can be probed using a broad set of experimentally accessible observables, including the entanglement entropy and the vacuum persistence amplitude.

quant-ph↗

arXiv2015

Proposal for the Quantum Simulation of the CP(2) Model on Optical Lattices

The 2d CP(N-1) models share a number of features with QCD, like asymptotic freedom, a dynamically generated mass gap and topological sectors. They have been formulated and analysed successfully in the framework of the so-called D-theory, which provides a smooth access to the continuum limit. In that framework, we propose an experimental set-up for the quantum simulation of the CP(2) model. It is based on ultra-cold Alkaline-Earth Atoms (AEAs) located on the sites of an optical lattice, where the nuclear spins represent the relevant degrees of freedom. We present numerical results for the correlation length and for the real time decay of a false vacuum, to be compared with such a future experiment. The latter could also enable the exploration of theta-vacua and of the phase diagram at finite chemical potentials, since it does not suffer from any sign problem.

hep-lat↗

arXiv2015

Stretched exponential decay of Majorana edge modes in many-body localized Kitaev chains under dissipation

We investigate the resilience of symmetry-protected topological edge states at the boundaries of Kitaev chains in the presence of a bath which explicitly introduces symmetry-breaking terms. Specifically, we focus on single-particle losses and gains, violating the protecting parity symmetry, which could generically occur in realistic scenarios. For homogeneous systems, we show that the Majorana mode decays exponentially fast. By the inclusion of strong disorder, where the closed system enters a many-body localized phase, we find that the Majorana mode can be stabilized substantially. The decay of the Majorana converts into a stretched exponential form for particle losses or gains occuring in the bulk. In particular, for pure loss dynamics we find a universal exponent $α\simeq 2/3$. We show that this holds both in the Anderson and many-body localized regimes. Our results thus provide a first step to stabilize edge states even in the presence of symmetry-breaking environments.

cond-mat.dis-nn↗

arXiv2015

Designing Frustrated Quantum Magnets with Laser-Dressed Rydberg Atoms

We show how a broad class of lattice spin-1/2 models with angular- and distance-dependent couplings can be realized with cold alkali atoms stored in optical or magnetic trap arrays. The effective spin-1/2 is represented by a pair of atomic ground states, and spin-spin interactions are obtained by admixing van der Waals interactions between fine-structure split Rydberg states with laser light. The strengths of the diagonal spin interactions as well as the "flip-flop", and "flip-flip" and "flop-flop" interactions can be tuned by exploiting quantum interference, thus realizing different spin symmetries. The resulting energy scales of interactions compare well with typical temperatures and decoherence time-scales, making the exploration of exotic forms of quantum magnetism, including emergent gauge theories and compass models, accessible within state-of-the-art experiments.

quant-ph↗

arXiv2015

Hexagonal Plaquette Spin-spin Interactions and Quantum Magnetism in a Two-dimensional Ion Crystal

We propose a trapped ion scheme en route to realize spin Hamiltonians on a Kagome lattice which, at low energies, are described by emergent Z2 gauge fields, and support a topological quantum spin liquid ground state. The enabling element in our scheme is the hexagonal plaquette spin-spin interactions in a 2D ion crystal. For this, the phonon-mode spectrum of the crystal is engineered by standing-wave optical potentials or by using Rydberg excited ions, thus generating localized phonon-modes around a hexagon of ions selected out of the entire two-dimensional crystal. These tailored modes can mediate spin-spin interactions between ion-qubits on a hexagonal plaquette when subject to state-dependent optical dipole forces. We discuss how these interactions can be employed to emulate a generalized Balents-Fisher-Girvin model in minimal instances of one and two plaquettes. This model is an archetypical Hamiltonian in which gauge fields are the emergent degrees of freedom on top of the classical ground state manifold. Under realistic situations, we show the emergence of a discrete Gauss's law as well as the dynamics of a deconfined charge excitation on a gauge-invariant background using the two-plaquettes trapped ions spin-system. The proposed scheme in principle allows further scaling in a future trapped ion quantum simulator, and we conclude that our work will pave the way towards the simulation of emergent gauge theories and quantum spin liquids in trapped ion systems.

cond-mat.quant-gas↗

arXiv2014

Quantum Spin Ice and dimer models with Rydberg atoms

Quantum spin ice represents a paradigmatic example on how the physics of frustrated magnets is related to gauge theories. In the present work we address the problem of approximately realizing quantum spin ice in two dimensions with cold atoms in optical lattices. The relevant interactions are obtained by weakly admixing van der Waals interactions between laser admixed Rydberg states to the atomic ground state atoms, exploiting the strong angular dependence of interactions between Rydberg p-states together with the possibility of designing step-like potentials. This allows us to implement Abelian gauge theories in a series of geometries, which could be demonstrated within state of the art atomic Rydberg experiments. We numerically analyze the family of resulting microscopic Hamiltonians and find that they exhibit both classical and quantum order by disorder, the latter yielding a quantum plaquette valence bond solid. We also present strategies to implement Abelian gauge theories using both s- and p-Rydberg states in exotic geometries, e.g. on a 4-8 lattice.

cond-mat.quant-gas↗