Contributor info: Prof. Andreas Läuchli

Amit Jamadagni Gangapuram, Andreas M. Läuchli, Cornelius Hempel

SciPost Phys. Core 7, 075 (2024) · published 26 November 2024 | Toggle abstract · pdf

Rapid advances in quantum computing technology lead to an increasing need for software simulators that enable both algorithm design and the validation of results obtained from quantum hardware. This includes calculations that aim at probing regimes of quantum advantage, where a quantum computer outperforms a classical computer in the same task. High performance computing (HPC) platforms play a crucial role as today's quantum devices already reach beyond the limits of what powerful workstations can model, but a systematic evaluation of the individual performance of the many offered simulation packages is lacking so far. In this Technical Review, we benchmark several software packages capable of simulating quantum dynamics with a special focus on HPC capabilities. We develop a containerized toolchain for benchmarking a large set of simulation packages on a local HPC cluster using different parallelisation capabilities, and compare the performance and system size-scaling for three paradigmatic quantum computing tasks. Our results can help finding the right package for a given simulation task and lay the foundation for a systematic community effort to benchmark and validate upcoming versions of existing and also newly developed simulation packages.

Jonathan D'Emidio, Alexander A. Eberharter, Andreas M. Läuchli

SciPost Phys. 15, 061 (2023) · published 14 August 2023 | Toggle abstract · pdf

The hunt for exotic quantum phase transitions described by emergent fractionalized degrees of freedom coupled to gauge fields requires a precise determination of the fixed point structure from the field theoretical side, and an extreme sensitivity to weak first-order transitions from the numerical side. Addressing the latter, we revive the classic definition of the order parameter in the limit of a vanishing external field at the transition. We demonstrate that this widely understood, yet so far unused approach provides a diagnostic test for first-order versus continuous behavior that is distinctly more sensitive than current methods. We first apply it to the family of $Q$-state Potts models, where the nature of the transition is continuous for $Q\leq4$ and turns (weakly) first order for $Q>4$, using an infinite system matrix product state implementation. We then employ this new approach to address the unsettled question of deconfined quantum criticality in the $S=1/2$ Néel to valence bond solid transition in two dimensions, focusing on the square lattice $J$-$Q$ model. Our quantum Monte Carlo simulations reveal that both order parameters remain finite at the transition, directly confirming a first-order scenario with wide reaching implications in condensed matter and quantum field theory.

Patrick H. Wilhelm, Thomas C. Lang, Mathias S. Scheurer, Andreas M. Läuchli

SciPost Phys. 14, 040 (2023) · published 20 March 2023 | Toggle abstract · pdf

Twisted double- and mono-bilayer graphene are graphene-based moiré materials hosting strongly correlated fermions in a gate-tunable conduction band with a topologically non-trivial character. Using unbiased exact diagonalization complemented by unrestricted Hartree-Fock calculations, we find that the strong electron-electron interactions lead to a non-coplanar magnetic state, which has the same symmetries as the tetrahedral antiferromagnet on the triangular lattice and can be thought of as a skyrmion lattice commensurate with the moiré scale, competing with a set of ferromagnetic, topological charge density waves featuring an approximate emergent O(3) symmetry, "rotating" the different charge density wave states into each other. Direct comparison with exact diagonalization reveals that the ordered phases are accurately described within the unrestricted Hartree-Fock approximation. Exhibiting a finite charge gap and Chern number $|C|=1$, the formation of charge density wave order which is intimately connected to a skyrmion lattice phase is consistent with recent experiments on these systems.

Michael Schuler, Louis-Paul Henry, Yuan-Ming Lu, Andreas M. Läuchli

SciPost Phys. 14, 001 (2023) · published 11 January 2023 | Toggle abstract · pdf

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 and quasiholes 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 (``onsite'') Ising ($\mathbb{Z}_2$) 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 confined, 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 condensed anyons in the explored phase diagram. In combination with large-scale quantum Monte Carlo simulations we measure unusually large critical exponents $\eta$ for the scaling of the correlation function at the continuous anyon condensation transitions, and we further identify lines of (weakly) first order transitions in the phase diagram. As an important additional 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 capturing the transition from a $\mathbb{Z}_2$ topological order to either $\mathbb{Z}_2$ symmetry broken phase, which is in excellent agreement with the numerical results.

Michael Schuler, Daniele De Bernardis, Andreas M. Läuchli, Peter Rabl

SciPost Phys. 9, 066 (2020) · published 9 November 2020 | Toggle abstract · pdf

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.