arXiv subjects

Karel Van Acoleyen

Publications and source records attributed to Karel Van Acoleyen.

At least 19 recordsLinked to original sources

arXiv2026

Finite-Element Matrix Product States for Continuum Models in One Dimension

We present a matrix product state framework for simulating one-dimensional quantum many-body systems in the continuum using non-orthogonal single-particle basis sets. By mapping the physical problem to an auxiliary computational space, we show that the resulting many-body overlap operator can be efficiently encoded as a matrix product operator for sufficiently localized orbitals, thereby generalizing a construction that first appeared in [arXiv:2405.10285]. This construction recasts the variational ground-state search into a generalized eigenvalue problem, which can be solved using a generalized density matrix renormalization group algorithm. As a primary application, we employ a first-order finite-element expansion to study the ground state properties of the Lieb-Liniger gas in the presence of inhomogeneities. This approach also provides a natural setting for exactly refining the lattice, thereby enabling multigrid optimization strategies for matrix product states.

quant-ph↗

arXiv2026

Fast projections of two-dimensional light patterns using acousto-optical deflectors

Precise and flexible control of structured light fields is essential for applications ranging from optical trapping and quantum simulation to microscopy and materials processing. Acousto-optical deflectors (AODs) are widely used in these settings due to their high speed, large damage threshold, and ability to generate steerable optical tweezers. Multi-tone driving offers a powerful alternative to slow sequential scanning, enabling the projection of complex patterns with high accuracy as rapid acoustic modulation averages out inter-spot interference. In two dimensions, however, intermodulation between tones in orthogonal AODs can reintroduce coherent artifacts. We present a fast, feedback-free AOD projection scheme based on an incommensurately staggered frequency lattice that intrinsically suppresses such artifacts. For separable two-dimensional target patterns, our method removes the need for scanning entirely, enabling substantially faster and highly accurate projections. We further extend the approach to non-separable images using a minimal scanning strategy that maintains rather high projection speeds. These results demonstrate that appropriately engineered multi-tone AOD driving offers an efficient and robust route to high-speed, high-fidelity generation of arbitrary intensity patterns.

physics.optics↗

arXiv2026

Direct energy dissipation measurements for a driven superfluid via the harmonic-potential theorem

We propose and experimentally demonstrate a method to directly measure energy dissipation for a linearly driven superfluid confined in a harmonic trap. The method relies on a perturbed version of the harmonic-potential theorem, according to which a potential perturbation - effectively acting as a stirrer - converts center-of-mass motional energy into internal energy. Energy conservation then enables a direct, quantitative determination of the dissipated energy from measurements of the macroscopic center-of-mass observables. Applying this method to a perturbed, driven Bose-Einstein condensate, we observe dissipation curves characteristic of superfluid flow, including a critical velocity that depends on the stirrer strength, consistent with previous studies. Our results are supported by mean-field simulations, which corroborate both the theoretical framework and the experimental findings.

cond-mat.quant-gas↗

arXiv2025

Real-time bubble nucleation and growth for false vacuum decay on the lattice

We revisit quantum false vacuum decay for the one-dimensional Ising model, focusing on the real-time nucleation and growth of true vacuum bubbles. Via matrix product state simulations, we demonstrate that for a wide range of parameters, the full time-dependent quantum state is well described by a Gaussian ansatz in terms of domain wall operators, with the associated vacuum bubble wave function evolving according to the linearized time-dependent variational principle. The emerging picture shows three different stages of evolution: an initial nucleation of small bubbles, followed by semi-classical bubble growth, which in turn is halted by the lattice phenomenon of Bloch oscillations. Furthermore, we find that the resonant bubble only plays a significant role in a certain region of parameter-space. However, when significant, it does lead to an approximately constant decay rate during the intermediate stage. Moreover, this rate is in quantitative agreement with the analytical result of Rutkevich (Phys. Rev. B 60, 14525) for which we provide an independent derivation based on the Gaussian ansatz.

cond-mat.stat-mech↗

arXiv2024

Hawking radiation on the lattice from Floquet and local Hamiltonian quench dynamics

We construct two free fermion lattice models exhibiting Hawking pair creation. Specifically, we consider the simplest case of a d=1+1 massless Dirac fermion, for which the Hawking effect can be understood in terms of a quench of the uniform vacuum state with a non-uniform Hamiltonian that interfaces modes with opposite chirality. For both our models we find that additional modes arising from the lattice discretization play a crucial role, as they provide the bulk reservoir for the Hawking radiation: the Hawking pairs emerge from fermions deep inside the Fermi sea scattering off the effective black hole horizon. Our first model combines local hopping dynamics with a translation over one lattice site, and we find the resulting Floquet dynamics to realize a causal horizon, with fermions scattering from the region outside the horizon. For our second model, which relies on a purely local hopping Hamiltonian, we find the fermions to scatter from the inside. In both cases, for Hawking temperatures up to the inverse lattice spacing we numerically find the resulting Hawking spectrum to be in perfect agreement with the Fermi-Dirac quantum field theory prediction.

quant-ph↗

arXiv2022

Entanglement scaling for $λϕ_2^4$

We study the $λϕ^4$ model in $0+2$ dimensions at criticality, and effectuate a simultaneous scaling of UV and IR physics. We demonstrate that the order parameter $ϕ$, the correlation length $ξ$ and quantities like $ϕ^3$ and the entanglement entropy exhibit useful double scaling properties. The calculations are performed with boundary matrix product state methods on tensor network representations of the partition function, though the technique is equally applicable outside the realm of tensor networks. We find the value $α_c=11.09698(31)$ for the critical point, improving on previous results.

hep-lat↗

arXiv2021

The Chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition

We study the phase diagram of the $(1+1)$-dimensional Gross-Neveu model with both $g_x^2(\barψψ)^2$ and $g_y^2(\barψiγ_5ψ)^2$ interaction terms on a spatial lattice. The continuous chiral symmetry, which is present in the continuum model when $g_x^2=g_y^2$, has a mixed 't~Hooft anomaly with the charge conservation symmetry, which guarantees the existence of a massless mode. However, the same 't~Hooft anomaly also implies that the continuous chiral symmetry is broken explicitly in our lattice model. Nevertheless, from numerical matrix product state simulations we find that, for certain parameters of the lattice model, the continuous chiral symmetry reemerges in the infrared fixed point theory, even at strong coupling. We argue that, to understand this phenomenon, it is crucial to go beyond mean-field theory (or, equivalently, beyond the leading order term in a $1/N$ expansion). Interestingly, on the lattice, the chiral Gross-Neveu model appears at a Landau-forbidden second order phase transition separating two distinct and unrelated symmetry-breaking orders. We point out the crucial role of two different 't Hooft anomalies or Lieb-Schultz-Mattis obstructions for this Landau-forbidden phase transition to occur.

hep-th↗

arXiv2021

Lattice regularisation and entanglement structure of the Gross-Neveu model

We construct a Hamiltonian lattice regularisation of the $N$-flavour Gross-Neveu model that manifestly respects the full $\mathsf{O}(2N)$ symmetry, preventing the appearance of any unwanted marginal perturbations to the quantum field theory. In the context of this lattice model, the dynamical mass generation is intimately related to the Coleman-Mermin-Wagner and Lieb-Schultz-Mattis theorem. In particular, the model can be interpreted as lying at the first order phase transition line between a trivial and symmetry-protected topological (SPT) phase, which explains the degeneracy of the elementary kink excitations. We show that our Hamiltonian model can be solved analytically in the large $N$ limit, producing the correct expression for the mass gap. Furthermore, we perform extensive numerical matrix product state simulations for $N=2$, thereby recovering the emergent Lorentz symmetry and the proper non-perturbative mass gap scaling in the continuum limit. Finally, our simulations also reveal how the continuum limit manifests itself in the entanglement spectrum. As expected from conformal field theory we find two conformal towers, one tower spanned by the linear representations of $\mathsf{O}(4)$, corresponding to the trivial phase, and the other by the projective (i.e. spinor) representations, corresponding to the SPT phase.

hep-lat↗

arXiv2019

Entanglement compression in scale space: from the multiscale entanglement renormalization ansatz to matrix product operators

The multiscale entanglement renormalization ansatz (MERA) provides a constructive algorithm for realizing wavefunctions that are inherently scale invariant. Unlike conformally invariant partition functions however, the finite bond dimension $χ$ of the MERA provides a cut-off in the fields that can be realized. In this letter, we demonstrate that this cut-off is equivalent to the one obtained when approximating a thermal state of a critical Hamiltonian with a matrix product operator (MPO) of finite bond dimension $χ$. This is achieved by constructing an explicit mapping between the isometries of a MERA and the local tensors of the MPO.

cond-mat.str-el↗

arXiv2019

A scaling hypothesis for matrix product states

We revisit the question of describing critical spin systems and field theories using matrix product states, and formulate a scaling hypothesis in terms of operators, eigenvalues of the transfer matrix, and lattice spacing in the case of field theories. Critical exponents and central charge are determined by optimizing the exponents such as to obtain a data collapse. We benchmark this method by studying critical Ising and Potts models, where we also obtain a scaling ansatz for the correlation length and entanglement entropy. The formulation of those scaling functions turns out to be crucial for studying critical quantum field theories on the lattice. For the case of $λϕ^4$ with mass $μ^2$ and lattice spacing $a$, we demonstrate a double data collapse for the correlation length $ δξ(μ,λ,D)=\tildeξ \left((α-α_c)(δ/a)^{-1/ν}\right)$ with $D$ the bond dimension, $δ$ the gap between eigenvalues of the transfer matrix, and $α_c=μ_R^2/λ$ the parameter which fixes the critical quantum field theory.

cond-mat.stat-mech↗

arXiv2018

Captain Einstein: a VR experience of relativity

Captain Einstein is a virtual reality (VR) movie that takes you on a boat trip in a world with a slow speed of light. This allows for a direct experience of the theory of special relativity, much in the same spirit as in the Mr. Tompkins adventure by George Gamow (1939). In this paper we go through the different relativistic effects (e.g. length contraction, time dilation, Doppler shift, light aberration) that show up during the boat trip and we explain how these effects were implemented in the 360 video production process. We also provide exercise questions that can be used - in combination with the VR movie - to gain insight and sharpen the intuition on the basic concepts of special relativity.

physics.pop-ph↗

arXiv2017

Real-time simulation of the Schwinger effect with Matrix Product States

Matrix Product States (MPS) are used for the simulation of the real-time dynamics induced by an electric quench on the vacuum state of the massive Schwinger model. For small quenches it is found that the obtained oscillatory behavior of local observables can be explained from the single-particle excitations of the quenched Hamiltonian. For large quenches damped oscillations are found and comparison of the late time behavior with the appropriate Gibbs states seems to give some evidence for the onset of thermalization. Finally, the MPS real-time simulations are explicitly compared with the semi-classical approach and, as expected, agreement is found in the limit of large quenches.

hep-lat↗

arXiv2017

Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks

It has been established that Matrix Product States can be used to compute the ground state and single-particle excitations and their properties of lattice gauge theories at the continuum limit. However, by construction, in this formalism the Hilbert space of the gauge fields is truncated to a finite number of irreducible representations of the gauge group. We investigate quantitatively the influence of the truncation of the infinite number of representations in the Schwinger model, one-flavour QED$_2$, with a uniform electric background field. We compute the two-site reduced density matrix of the ground state and the weight of each of the representations. We find that this weight decays exponentially with the quadratic Casimir invariant of the representation which justifies the approach of truncating the Hilbert space of the gauge fields. Finally, we compute the single-particle spectrum of the model as a function of the electric background field.

hep-lat↗

arXiv2016

Confinement and string breaking for QED$_2$ in the Hamiltonian picture

The formalism of matrix product states is used to perform a numerical study of 1+1 dimensional QED -- also known as the (massive) Schwinger model -- in the presence of an external static `quark' and `antiquark'. We obtain a detailed picture of the transition from the confining state at short interquark distances to the broken-string `hadronized' state at large distances and this for a wide range of couplings, recovering the predicted behavior both in the weak and strong coupling limit of the continuum theory. In addition to the relevant local observables like charge and electric field, we compute the (bipartite) entanglement entropy and show that subtraction of its vacuum value results in a UV-finite quantity. We find that both string formation and string breaking leave a clear imprint on the resulting entropy profile. Finally, we also study the case of fractional probe charges, simulating for the first time the phenomenon of partial string breaking.

hep-lat↗

arXiv2016

Hamiltonian simulation of the Schwinger model at finite temperature

Using Matrix Product Operators (MPO) the Schwinger model is simulated in thermal equilibrium. The variational manifold of gauge invariant MPO is constructed to represent Gibbs states. As a first application the chiral condensate in thermal equilibrium is computed and agreement with earlier studies is found. Furthermore, as a new application the Schwinger model is probed with a fractional charged static quark-antiquark pair separated infinitely far from each other. A critical temperature beyond which the string tension is exponentially suppressed is found, which is in qualitative agreement with analytical studies in the strong coupling limit. Finally, the CT symmetry breaking is investigated and our results strongly suggest that the symmetry is restored at any nonzero temperature.

hep-lat↗

arXiv2015

The entanglement of distillation for gauge theories

We study the entanglement structure of lattice gauge theories from the local operational point of view, and, similar to Soni and Trivedi (arXiv:1510.07455), we show that the usual entanglement entropy for a spatial bipartition can be written as the sum of an undistillable gauge part and of another part corresponding to the LOCC distillable entanglement, which is obtained by depolarizing the local superselection sectors. We demonstrate that the distillable entanglement is zero for pure abelian gauge theories in the weak coupling limit, while it is in general nonzero for the nonabelian case. We also consider gauge theories with matter, and show in a perturbative approach how area laws -- including a topological correction -- emerge for the distillable entanglement.

quant-ph↗

arXiv2015

Tensor networks for gauge field theories

Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular class of TNS and are used for the simulation of (1+1)-dimensional systems. In this proceeding we use MPS to determine the elementary excitations of the Schwinger model in the presence of an electric background field. We obtain an estimate for the value of the background field where the one-particle excitation with the largest energy becomes unstable and decays into two other elementary particles with smaller energy.

hep-lat↗

arXiv2015

Gauging quantum states: from global to local symmetries in many-body systems

We present an operational procedure to transform global symmetries into local symmetries at the level of individual quantum states, as opposed to typical gauging prescriptions for Hamiltonians or Lagrangians. We then construct a compatible gauging map for operators, which preserves locality and reproduces the minimal coupling scheme for simple operators. By combining this construction with the formalism of projected entangled-pair states (PEPS), we can show that an injective PEPS for the matter fields is gauged into a G-injective PEPS for the combined gauge-matter system, which potentially has topological order. We derive the corresponding parent Hamiltonian, which is a frustration free gauge theory Hamiltonian closely related to the Kogut-Susskind Hamiltonian at zero coupling constant. We can then introduce gauge dynamics at finite values of the coupling constant by applying a local filtering operation. This scheme results in a low-parameter family of gauge invariant states of which we can accurately probe the phase diagram, as we illustrate by studying a Z2 gauge theory with Higgs matter.

quant-ph↗