arXiv subjects

Andreas M. Läuchli

Publications and source records attributed to Andreas M. Läuchli.

At least 37 records · Page 2Linked to original sources

arXiv2022

Estimating heating times in periodically driven quantum many-body systems via avoided crossing spectroscopy

Periodic driving of a quantum (or classical) many-body system can alter the systems properties significantly and therefore has emerged as a promising way to engineer exotic quantum phases, such as topological insulators and discrete time crystals. A major limitation in such setups, is that generally interacting, driven systems will heat up over time and lose the desired properties. Understanding the relevant time scales is thus an important topic in the field and so far, there have only been few approaches to determine heating times for a concrete system quantitatively, and in a computationally efficient way. In this article we propose a new approach, based on building the heating rate from microscopic processes, encoded in avoided level crossings of the Floquet propagator. We develop a method able to resolve individual crossings and show how to construct the heating rate based on these. The method is closely related to the Fermi Golden Rule approach for weak drives, but can go beyond it, since it captures non-perturbative effects by construction. This enables our method to be applicable in scenarios such as the heating time of discrete time crystals or frequency dependent couplings, which are very relevant for Floquet engineering, where previously no efficient methods for estimating heating times were available.

cond-mat.stat-mech↗

arXiv2022

Dynamics of a pair of magnetic dipoles with nonreciprocal interactions due to a moving conductor

Recently it was demonstrated theoretically and experimentally that the presence of a moving conductor can break the reciprocity in the interactions between magnetic dipoles. In this article we investigate the influence of nonreciprocity on the dynamics of a pair of rigid XY dipoles, which have been realized in experiments. In particular, we focus on the energy nonconservation, which is a consequence of the nonreciprocity. We find that the dynamics indeed has regimes, wherein the kinetic energy grows quadratically. However, whether energy absorption occurs depends strongly on the initial conditions on the dipoles. Simulations for various initial conditions reveal an intricate dependence, resulting in a rich structure of the energy absorbing regime in the initial condition space. Nevertheless, we provide a qualitative explanation of these observations, interpreting the absence of energy absorption as a confinement of the dynamics in phase space.

cond-mat.other↗

arXiv2022

A Divide-and-Conquer Algorithm for Disordered and Interacting Few-Particle Systems in One Dimension

We present an algorithm to solve very large one-dimensional disordered and interacting few-particle systems. Our approach exploits the localized nature of the eigenfunctions in real space to achieve a linear scaling with the total system size $L$. This allows us to solve for all eigenfunctions of single-particle systems with different types of disorder up to one billion sites. Based on this technology we collect very detailed histograms of properties of eigenfunctions, such as the localization length or the participation ratio as a function of their energy. These histograms reveal surprisingly rich fine structures, whose origins we discuss. We also apply the algorithm to single particle problems where not all eigenfunctions are localized and show how this is diagnosed. Finally we extend the algorithm to interacting two-particle problems in the presence of disorder and demonstrate that our algorithm is well suited to analyze the effect of interactions on wavefunctions.

cond-mat.dis-nn↗

arXiv2022

Emergent XY* transition driven by symmetry fractionalization and anyon condensation

Anyons in a topologically ordered phase can carry fractional quantum numbers with respect to the symmetry group of the considered system, one example being the fractional charge of the quasiparticles in the fractional quantum Hall effect. When such symmetry-fractionalized anyons condense, the resulting phase must spontaneously break the symmetry and display a local order parameter. In this paper, we study the phase diagram and anyon condensation transitions of a $\mathbb{Z}_2$ topological order perturbed by Ising interactions in the Toric Code. The interplay between the global Ising symmetry and the lattice space group symmetries results in a non-trivial symmetry fractionalization class for the anyons, and is shown to lead to two characteristically different symmetry-broken phases. To understand the anyon condensation transitions, we use the recently introduced critical torus energy spectrum technique to identify a line of emergent 2+1D XY* transitions ending at a fine-tuned (Ising$^2$)* critical point. We provide numerical evidence for the occurrence of two symmetry breaking patterns predicted by the specific symmetry fractionalization class of the anyons in the explored phase diagram. In combination with quantum Monte Carlo simulations we measure unusually large critical exponents for the scaling of the correlation function at the anyon condensation transitions, and we identify lines of (weakly) first order transitions in the phase diagram. As an important result, we discuss the phase diagram of a resulting 2+1D Ashkin-Teller model, where we demonstrate that torus spectroscopy is capable of identifying emergent XY/O(2) critical behaviour, thereby solving some longstanding open questions in the domain of the 3D Ashkin-Teller models. To establish the generality of our results, we propose a field theoretical description which is in excellent agreement with the numerical results.

cond-mat.str-el↗

arXiv2022

Level statistics of the one-dimensional ionic Hubbard model

In this work we analyze the spectral level statistics of the one-dimensional ionic Hubbard model, the Hubbard model with an alternating on-site potential. In particular, we focus on the statistics of the gap ratios between consecutive energy levels. This quantity is often used in order to signal whether a many-body system is integrable or chaotic. A chaotic system has typically the statistics of a Gaussian ensemble of random matrices while the spectral properties of the integrable system follow a Poisson statistics. We find that whereas the Hubbard model without alternating potential is known to be integrable and its spectral properties follow a Poissonian statistics, the presence of an alternating potential causes a drastic change in the spectral properties which resemble the one of a Gaussian ensemble of random matrices. However, to uncover this behavior one has to separately consider the blocks of all symmetries of the ionic Hubbard model.

cond-mat.quant-gas↗

arXiv2022

Symmetric projected entangled-pair states analysis of a phase transition in coupled spin-1/2 ladders

Infinite projected entangled-pair states (iPEPS) have been introduced to accurately describe many-body wave functions on two-dimensional lattices. In this context, two aspects are crucial: the systematic improvement of the {\it Ansatz} by the optimization of its building blocks, i.e., tensors characterized by bond dimension $D$, and the extrapolation scheme to reach the "thermodynamic" limit $D \to \infty$. Recent advances in variational optimization and scaling based on correlation lengths demonstrated the ability of iPEPS to capture the spontaneous breaking of a continuous symmetry in phases such as the antiferromagnetic (Néel) phase with high fidelity, in addition to valence-bond solids which are already well described by finite-$D$ iPEPS. In contrast, systems in the vicinity of continuous quantum phase transitions still present a challenge for iPEPS, especially when non-abelian symmetries are involved. Here, we consider the iPEPS Ansatz to describe the continuous transition between the (gapless) antiferromagnet and the (gapped) paramagnet that exists in the $S=1/2$ Heisenberg model on coupled two-leg ladders. In particular, we show how accurate iPEPS results can be obtained down to a narrow interval around criticality and analyze the scaling of the order parameter in the Néel phase in a spatially anisotropic situation.

cond-mat.str-el↗

arXiv2021

Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point

We establish the universal torus low-energy spectra at the free Dirac fixed point and at the strongly coupled chiral Ising fixed point and their subtle crossover behaviour in the Gross-Neuveu-Yukawa field theory with ${n_\text{D}=4}$ component Dirac spinors in $D=(2+1)$ dimensions. These fixed points and the field theories are directly relevant for the long-wavelength physics of certain interacting Dirac systems, such as repulsive spinless fermions on the honeycomb lattice or $π$-flux square lattice. The torus energy spectrum has been shown previously to serve as a characteristic fingerprint of relativistic fixed points and is a powerful tool to discriminate quantum critical behaviour in numerical simulations. Here, we use a combination of exact diagonalization and quantum Monte Carlo simulations of strongly interacting fermionic lattice models, to compute the critical torus energy spectrum on finite-size clusters with periodic boundaries and extrapolate them to the thermodynamic limit. Additionally, we compute the torus energy spectrum analytically using the perturbative expansion in ${ε= 4 - D}$, which is in good agreement with the numerical results, thereby validating the presence of the chiral Ising fixed point in the lattice models at hand. We show that the strong interaction between the spinor field and the scalar order-parameter field strongly influences the critical torus energy spectrum and we observe prominent multiplicity features related to an emergent symmetry predicted from the quantum field theory. Building on these results we are able to address the subtle crossover physics of the low-energy spectrum flowing from the chiral Ising fixed point to the Dirac fixed point, and analyze earlier flawed attempts to extract Fermi velocity renormalizations from the low-energy spectrum.

cond-mat.str-el↗

arXiv2021

The Vacua of Dipolar Cavity Quantum Electrodynamics

The structure of solids and their phases is mainly determined by static Coulomb forces while the coupling of charges to the dynamical, i.e., quantized degrees of freedom of the electromagnetic field plays only a secondary role. Recently, it has been speculated that this general rule can be overcome in the context of cavity quantum electrodynamics (QED), where the coupling of dipoles to a single field mode can be dramatically enhanced. Here we present a first exact analysis of the ground states of a dipolar cavity QED system in the non-perturbative coupling regime, where electrostatic and dynamical interactions play an equally important role. Specifically, we show how strong and long-range vacuum fluctuations modify the states of dipolar matter and induce novel phases with unusual properties. Beyond a purely fundamental interest, these general mechanisms can be important for potential applications, ranging from cavity-assisted chemistry to quantum technologies based on ultrastrongly coupled circuit QED systems.

quant-ph↗

arXiv2021

Interplay of Fractional Chern Insulator and Charge-Density-Wave Phases in Twisted Bilayer Graphene

We perform an extensive exact diagonalization study of interaction driven insulators in spin- and valley-polarized moiré flat bands of twisted bilayer graphene aligned with its hexagonal boron nitride substrate. In addition to previously reported fractional Chern insulator phases, we provide compelling evidence for competing charge-density-wave phases at multiple fractional fillings of a realistic single-band model. A thorough analysis at different interlayer hopping parameters, motivated by experimental variability, and the role of kinetic energy at various Coulomb interaction strengths highlight the competition between these phases. The interplay of the single-particle and the interaction induced hole dispersion with the inherent Berry curvature of the Chern bands is intuitively understood to be the driving mechanism for the ground-state selection. The resulting phase diagram features remarkable agreement with experimental findings in a related moiré heterostructure and affirms the relevance of our results beyond the scope of graphene based materials.

cond-mat.str-el↗

arXiv2020

Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms

Quantum simulation using synthetic systems is a promising route to solve outstanding quantum many-body problems in regimes where other approaches, including numerical ones, fail. Many platforms are being developed towards this goal, in particular based on trapped ions, superconducting circuits, neutral atoms or molecules. All of which face two key challenges: (i) scaling up the ensemble size, whilst retaining high quality control over the parameters and (ii) certifying the outputs for these large systems. Here, we use programmable arrays of individual atoms trapped in optical tweezers, with interactions controlled by laser-excitation to Rydberg states to implement an iconic many-body problem, the antiferromagnetic 2D transverse field Ising model. We push this platform to an unprecedented regime with up to 196 atoms manipulated with high fidelity. We probe the antiferromagnetic order by dynamically tuning the parameters of the Hamiltonian. We illustrate the versatility of our platform by exploring various system sizes on two qualitatively different geometries, square and triangular arrays. We obtain good agreement with numerical calculations up to a computationally feasible size (around 100 particles). This work demonstrates that our platform can be readily used to address open questions in many-body physics.

quant-ph↗

arXiv2020

Valence bond solid and possible deconfined quantum criticality in an extended kagome lattice Heisenberg antiferromagnet

We present numerical evidence for the emergence of an extended valence bond solid (VBS) phase at $T=0$ in the kagome $S=1/2$ Heisenberg antiferromagnet with ferromagnetic further-neighbor interactions. The VBS is located at the boundary between two magnetically ordered regions and extends close to the nearest-neighbor Heisenberg point. It exhibits a diamond-like singlet covering pattern with a $12$-site unit-cell. Our results suggest the possibility of a direct, possibly continuous, quantum phase transition from the neighboring $\mathbf{q}=0$ coplanar magnetically ordered phase into the VBS phase. Moreover, a second phase which breaks lattice symmetries, and is of likely spin-nematic type, is found close to the transition to the ferromagnetic phase. The results have been obtained using numerical Exact Diagonalization. We discuss implications of our results on the nature of nearest-neighbor Heisenberg antiferromagnet.

cond-mat.str-el↗

arXiv2020

Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets

Quantum magnets with a large SU($N$) symmetry are a promising playground for the discovery of new forms of exotic quantum matter. Motivated by recent experimental efforts to study SU($N$) quantum magnetism in samples of ultracold fermionic alkaline-earth-like atoms in optical lattices, we study here the temperature dependence of spin correlations in the SU($N$) Heisenberg spin model in a wide range of temperatures. We uncover a sizeable regime in temperature, starting at $T=\infty$ down to intermediate temperatures and for all $N\ge2$, in which the correlations have a common spatial structure on a broad range of lattices, with the sign of the correlations alternating from one Manhattan shell to the next, while the amplitude of the correlations is rapidly decreasing with distance. Focussing on the one-dimensional chain and the two-dimensional square and triangular lattice for certain $N$, we discuss the appearance of a disorder and a Lifshitz temperature, separating the commensurate Manhattan high-$T$ regime from a low-$T$ incommensurate regime. We observe that this temperature window is associated to an approximately $N$-independent entropy reduction from the $\ln(N)$ entropy at infinite temperature. Our results are based on high-temperature series arguments and as well as large-scale numerical full diagonalization results of thermodynamic quantities for SU($3$) and SU($4$) square lattice samples, corresponding to a total Hilbert space of up to $4\times 10^9$ states.

cond-mat.quant-gas↗

arXiv2019

Comment on "The role of electron-electron interactions in two-dimensional Dirac fermions''

Tang et al. [Science 361, 570 (2018)] report on the properties of Dirac fermions with both on-site and Coulomb interactions. The substantial decrease up to ~40% of the Fermi velocity of Dirac fermions with on-site interaction is inconsistent with the numerical data near the Gross-Neveu quantum critical point. This results from an inappropriate finite-size extrapolation.

cond-mat.str-el↗

arXiv2019

The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited

We examine the perennial quantum spin-liquid candidate $S=1/2$ Heisenberg antiferromagnet on the kagome lattice. Our study is based on achieving Lanczos diagonalization of the Hamiltonian on a $48$ site cluster in sectors with dimensions as a large as $5 \times 10^{11}$. The results reveal novel intricate structures in the low-lying energy spectrum. These structures by no means unambiguously support an emerging consensus of a $\mathbb{Z}_2$ spin liquid ground state, but instead appear compatible with several scenarios, including four-fold topological degeneracy, inversion symmetry breaking and a combination thereof. We discuss finite-size effects, such as the apparent absence of ETH, and note that while considerably reduced, some are still present for the largest cluster. Finally, we observe that an XXZ model in the Ising limit reproduces remarkably well the most striking features of finite-size spectra.

cond-mat.str-el↗

arXiv2019

Floating Phases in One-Dimensional Rydberg Ising Chains

We report on the quantitative ground state phase diagram of a van der Waals interacting chain of Rydberg atoms. These systems are known to host crystalline phases locked to the underlying lattice as well as a gapped, disordered phase. We locate and characterize a third type of phase, the so called floating phase, which can be seen as a one-dimensional 'crystalline' phase which is not locked to the lattice. These phases have been theoretically predicted to exist in the phase diagram, but were not reported so far. Our results have been obtained using state-of-the-art numerical tensor network techniques and pave the way for the experimental exploration of floating phases with existing Rydberg quantum simulators.

cond-mat.quant-gas↗

arXiv2018

Sublattice Coding Algorithm and Distributed Memory Parallelization for Large-Scale Exact Diagonalizations of Quantum Many-Body Systems

We present algorithmic improvements for fast and memory-efficient use of discrete spatial symmetries in Exact Diagonalization computations of quantum many-body systems. These techniques allow us to work flexibly in the reduced basis of symmetry-adapted wave functions. Moreover, a parallelization scheme for the Hamiltonian-vector multiplication in the Lanczos procedure for distributed memory machines avoiding load balancing problems is proposed. We demonstrate that using these methods low-energy properties of systems of up to 50 spin-1/2 particles can be successfully determined.

cond-mat.str-el↗

arXiv2018

Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone

We present quantum Monte Carlo simulations for the chiral Heisenberg Gross-Neveu-Yukawa quantum phase transition of relativistic fermions with $N=4$ Dirac spinor components subject to a repulsive, local four fermion interaction in 2+1$d$. Here we employ a two dimensional lattice Hamiltonian with a single, spin-degenerate Dirac cone, which exactly reproduces a linear energy-momentum relation for all finite size lattice momenta in the absence of interactions. This allows us to significantly reduce finite size corrections compared to the widely studied honeycomb and $π$-flux lattices. A Hubbard term dynamically generates a mass beyond a critical coupling of ${U_c = 6.76(1)}$ as the system acquires antiferromagnetic order and SU(2) spin rotational symmetry is spontaneously broken. At the quantum phase transition we extract a self-consistent set of critical exponents ${ν= 0.98(1)}$, ${η_ϕ = 0.53(1)}$, ${η_ψ = 0.18(1)}$, ${β= 0.75(1)}$. We provide evidence for the continuous degradation of the quasi-particle weight of the fermionic excitations as the critical point is approached from the semimetallic phase. Finally we study the effective "speed of light" of the low-energy relativistic description, which depends on the interaction $U$, but is expected to be regular across the quantum phase transition. We illustrate that the strongly coupled bosonic and fermionic excitations share a common velocity at the critical point.

cond-mat.str-el↗

arXiv2018

Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions

It is an open question how well tensor network states in the form of an infinite projected entangled pair states (iPEPS) tensor network can approximate gapless quantum states of matter. Here we address this issue for two different physical scenarios: i) a conformally invariant $(2+1)d$ quantum critical point in the incarnation of the transverse field Ising model on the square lattice and ii) spontaneously broken continuous symmetries with gapless Goldstone modes exemplified by the $S=1/2$ antiferromagnetic Heisenberg and XY models on the square lattice. We find that the energetically best wave functions display {\em finite} correlation lengths and we introduce a powerful finite correlation length scaling framework for the analysis of such finite-$D$ iPEPS states. The framework is important i) to understand the mild limitations of the finite-$D$ iPEPS manifold in representing Lorentz-invariant, gapless many body quantum states and ii) to put forward a practical scheme in which the finite correlation length $ξ(D)$ combined with field theory inspired formulae can be used to extrapolate the data to infinite correlation length, i.e. to the thermodynamic limit. The finite correlation length scaling framework opens the way for further exploration of quantum matter with an (expected) Lorentz-invariant, massless low-energy description, with many applications ranging from condensed matter to high-energy physics.

cond-mat.str-el↗