Publications

Order by: publication date number of citations

• QDarts: A quantum dot array transition simulator for finding charge transitions in the presence of finite tunnel couplings, non-constant charging energies and sensor dots

  Jan A. Krzywda, Weikun Liu, Evert van Nieuwenburg, Oswin Krause

  SciPost Phys. Codebases 43 (2025) · published 9 January 2025 | Toggle abstract · pdf

  We present QDarts, an efficient simulator for realistic charge stability diagrams of quantum dot array (QDA) devices in equilibrium states. It allows for pinpointing the location of concrete charge states and their transitions in a high-dimensional voltage space (via arbitrary two-dimensional cuts through it), and includes effects of finite tunnel coupling, non-constant charging energy and a simulation of noisy sensor dots. These features enable close matching of various experimental results in the literature, and the package hence provides a flexible tool for testing QDA experiments, as well as opening the avenue for developing new methods of device tuning.

  1 citation

• Entanglement flow in the Kane-Fisher quantum impurity problem

  Chunyu Tan, Yuxiao Hang, Stephan Haas, Hubert Saleur

  SciPost Phys. Core 8, 002 (2025) · published 8 January 2025 | Toggle abstract · pdf

  The problem of a local impurity in a Luttinger liquid, just like the anisotropic Kondo problem (of which it is technically a cousin), describes many different physical systems. As shown by Kane and Fisher, the presence of interactions profoundly modifies the physics familiar from Fermi liquid theory, and leads to non-intuitive features, best described in the Renormalization Group language (RG), such as flows towards healed or split fixed points. While this problem has been studied for many years using more traditional condensed matter approaches, it remains somewhat mysterious from the point of view of entanglement, both for technical and conceptual reasons. We propose and explore in this paper a new way to think of this important aspect. We use the realization of the Kane Fisher universality class provided by an XXZ spin chain with a modified bond strength between two sites, and explore the difference of (Von Neumann) entanglement entropies of a region of length $\ell$ with the rest of the system - to which it is connected with a modified bond - in the cases when $\ell$ is even and odd. Surprisingly, we find out that this difference $\delta S\equiv S^e-S^o$ remains of $O(1)$ in the thermodynamic limit, and gives rise now, depending on the sign of the interactions, to "resonance" curves, interpolating between $-\ln 2$ and $0$, and depending on the product $\ell T_B$, where $1/T_B$ is a characteristic length scale akin to the Kondo length in Kondo problems. $\delta S$ can be interpreted as a measure of the hybridization of the left-over spin in odd length subsystems with the "bath" constituted by the rest of the chain. The problem is studied both numerically using DMRG and analytically near the healed and split fixed points. Interestingly - and in contrast with what happens in other impurity problems - $\delta S$ can, at least to lowest order, be tackled by conformal perturbation theory.

• Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods

  Raphaël Photopoulos, Antoine Boulet

  SciPost Phys. 18, 003 (2025) · published 6 January 2025 | Toggle abstract · pdf

  Introducing low-energy effective Hamiltonians is usual to grasp most correlations in quantum many-body problems. For instance, such effective Hamiltonians can be treated at the mean-field level to reproduce some physical properties of interest. Employing effective Hamiltonians that contain many-body correlations renders the use of perturbative many-body techniques difficult because of the overcounting of correlations. In this work, we develop a strategy to apply an extension of the many-body perturbation theory starting from an effective interaction that contains correlations beyond the mean-field level. The goal is to re-organize the many-body calculation to avoid the overcounting of correlations originating from the introduction of correlated effective Hamiltonians in the description. For this purpose, we generalize the formulation of the Rayleigh-Schrödinger perturbation theory by including free parameters adjusted to reproduce the appropriate limits. In particular, the expansion in the bare weak-coupling regime and the strong-coupling limit serves as a valuable input to fix the value of the free parameters appearing in the resulting expression. This method avoids double counting of correlations using beyond-mean-field strategies for the description of many-body systems. The ground state energy of various systems relevant for ultracold atomic, nuclear, and condensed matter physics is reproduced qualitatively beyond the domain of validity of the standard many-body perturbation theory. Finally, our method suggests interpreting the formal results obtained as an effective field theory using the proposed reorganization of the many-body calculation. The results, like ground state energies, are improved systematically by considering higher orders in the extended many-body perturbation theory while maintaining a straightforward polynomial expansion.

• Topologically ordered steady states in open quantum systems

  Zijian Wang, Xu-Dong Dai, He-Ran Wang, Zhong Wang

  SciPost Phys. 17, 167 (2024) · published 13 December 2024 | Toggle abstract · pdf

  The interplay between dissipation and correlation can lead to novel emergent phenomena in open systems. Here we investigate "steady-state topological order" defined by the robust topological degeneracy of steady states, which is a generalization of the ground-state topological degeneracy of closed systems. Specifically, we construct two representative Liouvillians using engineered dissipation, and exactly solve the steady states with topological degeneracy. We find that while the steady-state topological degeneracy is fragile under noise in two dimensions, it is stable in three dimensions, where a genuine many-body phase with topological degeneracy is realized. We identify universal features of steady-state topological physics such as the deconfined emergent gauge field and slow relaxation dynamics of topological defects. The transition from a topologically ordered phase to a trivial phase is also investigated via numerical simulation. Our work highlights the essential difference between ground-state topological order in closed systems and steady-state topological order in open systems.

  1 citation

• When does a Fermi puddle become a Fermi sea? Emergence of pairing in two-dimensional trapped mesoscopic Fermi gases

  Emma K. Laird, Brendan C. Mulkerin, Jia Wang, Matthew J. Davis

  SciPost Phys. 17, 163 (2024) · published 11 December 2024 | Toggle abstract · pdf

  Pairing lies at the heart of superfluidity in fermionic systems. Motivated by recent experiments in mesoscopic Fermi gases, we study up to six fermionic atoms with equal masses and equal populations in two different spin states, confined in a quasi-two-dimensional harmonic trap. We couple a stochastic variational approach with the use of an explicitly correlated Gaussian basis set, which enables us to obtain highly accurate energies and structural properties. Utilising two-dimensional two-body scattering theory with a finite-range Gaussian interaction potential, we tune the effective range to model realistic quasi-two-dimensional scattering. We calculate the excitation spectrum, pair correlation function, and number of pairs as a function of increasing attractive interaction strength. For up to six fermions in the ground state, we find that opposite spin and momentum pairing is maximised well below the Fermi surface in momentum space. By contrast, corresponding experiments on twelve fermions have found that pairing is maximal at the Fermi surface and strongly suppressed beneath [M. Holten et al., Nature 606, 287-291 (2022)]. This suggests that the Fermi sea — which acts to suppress pairing at low momenta via Pauli blocking — emerges in the transition from six to twelve particles.

• Dynamical correlation functions in the Ising field theory

  István Csépányi, Márton Kormos

  SciPost Phys. 17, 162 (2024) · published 10 December 2024 | Toggle abstract · pdf

  We study finite temperature dynamical correlation functions of the magnetization operator in the one-dimensional Ising quantum field theory. Our approach is based on a finite temperature form factor series and on a Fredholm determinant representation of the correlators. While for space-like separations the Fredholm determinant can be efficiently evaluated numerically, for the time-like region it has convergence issues inherited from the form factor series. We develop a method to compute the correlation functions at time-like separations based on the analytic continuation of the space-time coordinates to complex values. Using this numerical technique, we explore all space-time and temperature regimes in both the ordered and disordered phases including short, large, and near-light-cone separations at low and high temperatures. We confirm the existing analytic predictions for the asymptotic behavior of the correlations except in the case of space-like correlations in the paramagnetic phase. For this case we derive a new closed form expression for the correlation length that has some unusual properties: it is a non-analytic function of both the space-time direction and the temperature, and its temperature dependence is non-monotonic.

• Complexity is not enough for randomness

  Shiyong Guo, Martin Sasieta, Brian Swingle

  SciPost Phys. 17, 151 (2024) · published 4 December 2024 | Toggle abstract · pdf

  We study the dynamical generation of randomness in Brownian systems as a function of the degree of locality of the Hamiltonian. We first express the trace distance to a unitary design for these systems in terms of an effective equilibrium thermal partition function, and provide a set of conditions that guarantee a linear time to design. We relate the trace distance to design to spectral properties of the time-evolution operator. We apply these considerations to the Brownian $p$-SYK model as a function of the degree of locality $p$. We show that the time to design is linear, with a slope proportional to $1/p$. We corroborate that when $p$ is of order the system size this reproduces the behavior of a completely non-local Brownian model of random matrices. For the random matrix model, we reinterpret these results from the point of view of classical Brownian motion in the unitary manifold. Therefore, we find that the generation of randomness typically persists for exponentially long times in the system size, even for systems governed by highly non-local time-dependent Hamiltonians. We conjecture this to be a general property: there is no efficient way to generate approximate Haar random unitaries dynamically, unless a large degree of fine-tuning is present in the ensemble of time-dependent Hamiltonians. We contrast the slow generation of randomness to the growth of quantum complexity of the time-evolution operator. Using known bounds on circuit complexity for unitary designs, we obtain a lower bound determining that complexity grows at least linearly in time for Brownian systems. We argue that these bounds on circuit complexity are far from tight and that complexity grows at a much faster rate, at least for non-local systems.

  2 citations

• Benchmarking quantum computer simulation software packages: State vector simulators

  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.

  1 citation

• Comparative microscopic study of entropies and their production

  Philipp Strasberg, Joseph Schindler

  SciPost Phys. 17, 143 (2024) · published 25 November 2024 | Toggle abstract · pdf

  We study the time evolution of eleven microscopic entropy definitions (of Boltzmann-surface, Gibbs-volume, canonical, coarse-grained-observational, entanglement and diagonal type) and three microscopic temperature definitions (based on Boltzmann, Gibbs or canonical entropy). This is done for the archetypal nonequilibrium setup of two systems exchanging energy, modeled here with random matrix theory, based on numerical integration of the Schrödinger equation. We consider three types of pure initial states (local energy eigenstates, decorrelated and entangled microcanonical states) and three classes of systems: (A) two normal systems, (B) a normal and a negative temperature system and (C) a normal and a negative heat capacity system. We find: (1) All types of initial states give rise to the same macroscopic dynamics. (2) Entanglement and diagonal entropy sensitively depend on the microstate, in contrast to all other entropies. (3) For class B and C, Gibbs-volume entropies can violate the second law and the associated temperature becomes meaningless. (4) For class C, Boltzmann-surface entropies can violate the second law and the associated temperature becomes meaningless. (5) Canonical entropy has a tendency to remain almost constant. (6) For a Haar random initial state, entanglement or diagonal entropy behave similar or identical to coarse-grained-observational entropy.

  2 citations

• Boundary chaos: Spectral form factor

  Felix Fritzsch, Tomaž Prosen

  SciPost Phys. 17, 142 (2024) · published 22 November 2024 | Toggle abstract · pdf

  Random matrix spectral correlations is a defining feature of quantum chaos. Here, we study such correlations in a minimal model of chaotic many-body quantum dynamics where interactions are confined to the system's boundary, dubbed boundary chaos, in terms of the spectral form factor and its fluctuations. We exactly calculate the latter in the limit of large local Hilbert space dimension $q$ for different classes of random boundary interactions and find it to coincide with random matrix theory, possibly after a non-zero Thouless time. The latter effect is due to a drastic enhancement of the spectral form factor, when integer time and system size fulfill a resonance condition. We compare our semiclassical (large $q$) results with numerics at small local Hilbert space dimension ($q=2,3$) and observe qualitatively similar features as in the semiclassical regime.