arXiv subjects

Joachim Brand

Publications and source records attributed to Joachim Brand.

At least 19 recordsLinked to original sources

arXiv2026

Rimu.jl: Random integrators for many-body quantum systems

Rimu$.$jl is a Julia package for solving many-body quantum problems. The core of the package is a matrix-free implementation of Hamiltonians and other operators and compact representation of Fock states, which together allow for efficient methods suitable for high-performance computing. Rimu$.$jl includes a Julia implementation of the full configuration interaction quantum Monte Carlo (FCIQMC) algorithm which is a type of projector QMC algorithm for stochastically solving the time-independent Schrödinger equation. It also includes many well-known model Hamiltonians, and an interface for exact diagonalisation based on external eigenvalue solvers. Both the stochastic and exact diagonalisation methods are accessed with a CommonSolve$.$jl interface. We describe the FCIQMC algorithm and how to obtain estimators of observables as well as the key features of the implementation.

physics.comp-ph↗

arXiv2026

Quartic level repulsion in a quantum chaotic three-body system without symplectic symmetry

Among the fundamental symmetry classes of quantum chaotic systems in Dyson's threefold way, the symplectic class is rarely observed in nature. Characterized by the strongest possible level repulsion in the energy spectrum, the symplectic symmetry class also implies a double (Kramers) degeneracy of levels. Studying the spectral statistics of three quantum particles (identical bosons or mass-imbalanced fermions) in a harmonic trap, we find numerical evidence for strong level repulsion in the regime of weak contact interactions. While the statistical indicators are consistent with quantum chaos in systems with symplectic symmetry, the absence of Kramers degeneracy rules out this symmetry. In the strongly-interacting unitary limit either Poissonian or stick statistics are observed (depending on commensurability of the mass ratio) indicating regular dynamics.

cond-mat.quant-gas↗

arXiv2026

Scale invariance of the polaron energy at the Mott-superfluid critical point

Continuous quantum phase transitions are characterized by an order parameter and correlation functions that are often challenging to access experimentally or in direct numerical simulations. The energy of an added impurity can on the other hand be probed by established polaron spectroscopy, or numerically with Monte Carlo methods. We provide evidence from ground-state quantum Monte Carlo calculations that the energy of a mobile impurity interacting weakly with a surrounding lattice Bose gas provides access to the critical behavior of the Mott insulator-superfluid phase transition. Finite-size scaling of the energy reveals that its value is scale invariant at the critical point of the quantum phase transition, and we extract a scaling exponent that is currently unexplained by theory. For a small lattice we further observe a flattening of the impurity-boson density-density correlations at the critical point, which hints at a divergence of a corresponding length scale in the thermodynamic limit. Our results suggest that impurity spectroscopy represents a useful way to probe the critical properties of quantum phase transitions in general.

cond-mat.quant-gas↗

arXiv2025

Bound excited states of Fröhlich polarons in one dimension

The one-dimensional Fröhlich model describing the motion of a single electron interacting with optical phonons is a paradigmatic model of quantum many-body physics. We predict the existence of an arbitrarily large number of bound excited states in the strong coupling limit and calculate their excitation energies. Numerical simulations of a discretized model demonstrate the complete amelioration of the projector Monte Carlo sign problem by walker annihilation in an infinite Hilbert space. They reveal the threshold for the occurrence of the first bound excited states at a value of $α\approx 1.73$ for the dimensionless coupling constant. This puts the threshold into the regime of intermediate interaction strength. We find a significant spectral weight and increased phonon number of the bound excited state at threshold.

math-ph↗

arXiv2025

Effective theory for strongly attractive one-dimensional fermions

We study a one-dimensional system of two-component fermions in the limit of strong attractive particle-particle interactions. First, we analyze scattering in the corresponding few-body problem, which is analytically solvable via Bethe ansatz. This allows us to engineer effective interactions between the system's effective degrees of freedom: fermions and bosonic dimers (tightly bound pairs of fermions). We argue that, although these interactions are strong, the resulting effective problem can be mapped onto a weakly interacting one, paving the way for the use of perturbation theory. This finding simplifies studies of many-fermion systems under confinement that are beyond reach of state-of-the-art numerical methods. We illustrate this statement by considering an impurity atom in a Fermi gas.

cond-mat.quant-gas↗

arXiv2024

Lattice Bose polarons at strong coupling and quantum criticality

We develop a new theoretical framework for exploring a mobile impurity interacting strongly with a highly correlated bath of bosons in the quantum critical regime of a Mott insulator (MI) to superfluid (SF) quantum phase transition. Our framework is based on a powerful quantum Gutzwiller (QGW) description of the bosonic bath combined with diagrammatic field theory for the impurity-bath interactions. By resumming a selected class of diagrams to infinite order, a rich picture emerges where the impurity is dressed by the fundamental modes of the bath, which change character from gapped particle-hole excitations in the MI to Higgs and gapless Goldstone modes in the SF. This gives rise to the existence of several quasiparticle (polaron) branches with properties reflecting the strongly correlated environment. In particular, one polaron branch exhibits a sharp cusp in its energy, while a new ground-state polaron emerges at the $O(2)$ quantum phase transition point for integer filling, which reflects the nonanalytic behavior at the transition and the appearance of the Goldstone mode in the SF phase. Smooth versions of these features are inherited in the polaron spectrum away from integer filling because of the varying ``Mottness" of the bosonic bath. We furthermore compare our diagrammatic results with quantum Monte Carlo calculations, obtaining excellent agreement. This accuracy is quite remarkable for such a highly non-trivial case of strong interactions between the impurity and bosons in a maximally correlated quantum critical regime, and it establishes the utility of our framework. Finally, our results show how impurities can be used as quantum sensors and highlight fundamental differences between experiments performed at a fixed particle number or a fixed chemical potential.

cond-mat.quant-gas↗

arXiv2024

Swallow-tail dispersions of moving solitons in a two-dimensional fermionic superfluid

Soliton-like localised wave solutions in a two-dimensional Fermi superfluid are studied by solving the Bogoliubov-de Gennes equations in the BCS regime of weak pairing interactions. The dispersion relations of these solitons are found to exhibit a peculiar swallow-tail shape, with cusps and multiple branches. The effective mass of the solitons is found to diverge and change sign at the cusp. This behavior is in contrast to the smooth dispersion relations and negative effective masses of solitons in the three-dimensional Fermi superfluid. The swallow-tail dispersion relations are shown to be a consequence of counterflow of the superfluid and sign-changing contributions to the superfluid current from different transverse momenta in the Bogoliubov-de Gennes formalism. The results are relevant for the understanding of solitonic excitations in two-dimensional Fermi superfluids, such as ultracold atomic gases and high-temperature superconductors.

cond-mat.quant-gas↗

arXiv2023

Distributed vorticity model for vortex molecule dynamics

We analyze the effect of a hard wall trapping potential on the dynamics of a vortex molecule in a two-component Bose-Einstein condensate with linear coherent coupling. A vortex molecule consists of a vortex of the same charge in each component condensate connected by a domain wall of the relative phase. In a previous paper Ref.[Phys. RevA. 106,043319(2022)] we described the interaction of a vortex molecule with the boundary using the method of images by separately treating each component vortex as a point vortex, in addition to a Magnus force effect from the surface tension of the domain wall. Here we extend the model by considering a continuous distribution of image vorticity reflecting the effect of the domain wall on the vortex molecule phase structure. In the case of a precessing centered vortex molecule in an isotropic trap, distributing the image vorticity weakens its contribution to the precession frequency. We test the model predictions against numerical simulations of the coupled Gross-Pitaevskii equations in a two-dimensional circular disc and find support for the improved model.

cond-mat.quant-gas↗

arXiv2023

Andreev bound states at boundaries of polarized 2D Fermi superfluids with s-wave pairing and spin-orbit coupling

A topological superfluid phase characterized by an emergent chiral-p-wave pair potential is expected to form in a two-dimensional Fermi superfluid subject to s-wave pairing, spin-orbit coupling and a large-enough Zeeman splitting. Andreev bound states appear at phase boundaries, including Majorana zero modes whose existence is assured by the bulk-boundary correspondence principle. Here we study the physical properties of these subgap-energy bound states at step-like interfaces using the spin-resolved Bogoliubov-deGennes mean-field formalism and assuming small spin-orbit coupling. Extending a recently developed spin-projection technique based on Feshbach partitioning [SciPost Phys. 5, 016 (2018)] combined with the Andreev approximation allows us to obtain remarkably simple analytical expressions for the bound-state energies as well as the majority and minority spin components of their wave functions. Besides the vacuum boundary, where a majority-spin Majorana excitation is encountered, we also consider the boundary between the topological and a nontopological superfluid phase that can appear in a coexistence scenario due to the first-order topological phase transition predicted for this system. At this superfluid-superfluid interface, we find a localized chiral Majorana mode hosted by the minority-spin sector. Our theory further predicts majority-spin subgap-energy bound states similar to those found at a Josephson junction between same-chirality p-wave superfluids. Their presence affects the Majorana mode due to a coupling of minority and majority spin sectors only in the small energy range where their spectra overlap. Our results may inform experimental efforts aimed at realizing and characterizing unconventional Majorana quasiparticles.

cond-mat.quant-gas↗

arXiv2022

Rotational pendulum dynamics of a vortex molecule in a channel geometry

A vortex molecule is a topological excitation in two coherently coupled superfluids consisting of a vortex in each superfluid connected by a domain wall of the relative phase, also known as a Josephson vortex. We investigate the dynamics of this excitation in a quasi-two-dimensional geometry with slab or channel boundary conditions using an extended point vortex framework complemented by Gross-Pitaevskii simulations. Apart from translational motion along the channel, the vortex molecule is found to exhibit intriguing internal dynamics including rotation and rotational-pendulum-like dynamics. Trajectories leading to a boundary-induced break-up of the vortex molecule are also described qualitatively by the simplified model. We classify the stable and unstable fixed points as well as separatrices that characterize the vortex molecule dynamics.

cond-mat.quant-gas↗

arXiv2022

Stochastic differential equation approach to understanding the population control bias in full configuration interaction quantum Monte Carlo

We investigate a systematic statistical bias found in full configuration quantum Monte Carlo (FCIQMC) that originates from controlling a walker population with a fluctuating shift parameter. This bias can become the dominant error when the sign problem is absent, e.g. in bosonic systems. FCIQMC is a powerful statistical method for obtaining information about the ground state of a sparse and abstract matrix. We show that, when the sign problem is absent, the shift estimator has the nice property of providing an upper bound for the exact ground state energy and all projected energy estimators, while a variational estimator is still an upper bound to the exact energy with substantially reduced bias. A scalar model of the general FCIQMC population dynamics leads to an exactly solvable Itô stochastic differential equation. It provides further insights into the nature of the bias and gives accurate analytical predictions for delayed cross-covariance and auto-covariance functions of the shift energy estimator and the walker number. The model provides a toe-hold on finding a cure for the population control bias. We provide evidence for non-universal power-law scaling of the population control bias with walker number in the Bose-Hubbard model for various estimators of the ground state energy based on the shift or on projected energies. For the specific case of the non-interacting Bose-Hubbard Hamiltonian we obtain a full analytical prediction for the bias of the shift energy estimator.

cond-mat.quant-gas↗

arXiv2022

Triplet character of 2D-fermion dimers arising from $s$-wave attraction via spin-orbit coupling and Zeeman splitting

We theoretically study spin-$1/2$ fermions confined to two spatial dimensions and experiencing isotropic short-range attraction in the presence of both spin-orbit coupling and Zeeman spin splitting - a prototypical system for developing topological superfluidity in the many-body sector. Exact solutions for two-particle bound states are found to have a triplet contribution that dominates over the singlet part in an extended region of parameter space where the combined Zeeman- and center-of-mass-motion-induced spin-splitting energy is large. The triplet character of dimers is purest in the regime of weak $s$-wave interaction strength. Center-of-mass momentum is one of the parameters determining the existence of bound states, which we map out for both two- and one-dimensional types of spin-orbit coupling. Distinctive features emerging in the orbital part of the bound-state wave function, including but not limited to its $p$-wave character, provide observable signatures of unconventional pairing.

cond-mat.quant-gas↗

arXiv2022

Magnetic impurity in a one-dimensional few-fermion system

We present a numerical analysis of spin-$\frac{1}{2}$ fermions in a one-dimensional harmonic potential in the presence of a magnetic point-like impurity at the center of the trap. The model represents a few-body analogue of a magnetic impurity in the vicinity of an $s$-wave superconductor. Already for a few particles we find a ground-state level crossing between sectors with different fermion parities. We interpret this crossing as a few-body precursor of a quantum phase transition, which occurs when the impurity `breaks' a Cooper pair. This picture is further corroborated by analyzing density-density correlations in momentum space. Finally, we discuss how the system may be realized with existing cold-atoms platforms.

cond-mat.quant-gas↗

arXiv2022

Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity

We present exact numerical data for the lowest-energy momentum eigenstates (yrast states) of a repulsive spin impurity in a one-dimensional Bose gas using full configuration interaction quantum Monte Carlo (FCIQMC). As a stochastic extension to exact diagonalization it is well suited for the study of yrast states of a lattice-renormalized model for a quantum gas. Yrast states carry valuable information about the dynamic properties of slow-moving mobile impurities immersed in a many-body system. Based on the energies and the first and second order correlation functions of yrast states, we identify different dynamical regimes and the transitions between them: The polaron regime, where the impurity's motion is affected by the Bose gas through a renormalized effective mass; a regime of a gray soliton that is weakly correlated with a stationary impurity, and the depleton regime, where the impurity occupies a dark or gray soliton. Extracting the depleton effective mass reveals a super heavy regime where the magnitude of the (negative) depleton mass exceeds the mass of the finite Bose gas.

cond-mat.quant-gas↗

arXiv2020

Signatures of the BCS-BEC crossover in the yrast spectra of Fermi quantum rings

We study properties of the lowest energy states at non-zero total momentum (yrast states) of the Hubbard model for spin-1/2 fermions in the quantum ring configuration with attractive on-site interaction at low density. In the one-dimensional (1D) case we solve the Hubbard model using the Bethe ansatz, while for the crossover into the 2D regime we use the Full-Configuration-Interaction Quantum Monte-Carlo method (FCIQMC) to obtain the yrast states for the spin-balanced Fermi system. We show how the yrast excitation spectrum changes from the 1D to the 2D regime and how pairing affects the yrast spectra. We also find signatures of fragmented condensation for certain yrast states usually associated with dark solitons.

cond-mat.quant-gas↗

arXiv2020

Eliminating the wave function singularity for ultracold atoms by similarity transformation

A hyperbolic singularity in the wave-function of $s$-wave interacting atoms is the root problem for any accurate numerical simulation. Here we apply the transcorrelated method, whereby the wave-function singularity is explicitly described by a two-body Jastrow factor, and then folded into the Hamiltonian via a similarity transformation. The resulting non-singular eigenfunctions are approximated by stochastic Fock-space diagonalisation with energy errors scaling with $1/M$ in the number $M$ of single-particle basis functions. The performance of the transcorrelated method is demonstrated on the example of strongly correlated fermions with unitary interactions. The current method provides the most accurate ground state energies so far for three and four fermions in a rectangular box with periodic boundary conditions.

cond-mat.quant-gas↗

arXiv2020

Improved walker population control for full configuration interaction quantum Monte Carlo

Full configuration interaction quantum Monte Carlo (FCIQMC) is a stochastic approach for finding the ground state of a quantum many-body Hamiltonian. It is based on the dynamical evolution of a walker population in Hilbert space, which samples the ground state configuration vector over many iterations. Here we present a modification of the original protocol for walker population control of Booth et al. JCP 131, 054106 (2009) in order to achieve equilibration at a pre-defined average walker number and to avoid walker number overshoots. The dynamics of the walker population is described by a noisy damped harmonic oscillator and controlled by two parameters responsible for damping and forcing, respectively, for which reasonable values are suggested. We further introduce a population growth witness that can be used to detect annihilation plateaus related to overcoming the FCIQMC sign problem. Features of the new population control procedure such as precise walker number control and fast equilibration are demonstrated. The standard error of the shift estimator for the ground state energy as well as the population control bias are found to be unaffected by the population control procedure or its parameters. The improved control of the walker number, and thereby memory consumption, is a desirable feature required for automating FCIQMC calculations and requires minimal modifications to existing code.

cond-mat.quant-gas↗

arXiv2019

Quantum dark solitons in the one-dimensional Bose gas

Dark and grey soliton-like states are shown to emerge from numerically constructed superpositions of translationally-invariant eigenstates of the interacting Bose gas in a toroidal trap. The exact quantum many-body dynamics reveals a density depression with superdiffusive spreading that is absent in the mean-field treatment of solitons. A simple theory based on finite-size bound states of holes with quantum-mechanical center-of-mass motion quantitatively explains the time-evolution of the superposition states and predicts quantum effects that could be observed in ultra-cold gas experiments. The soliton phase step is shown to be a key ingredient of an accurate finite size approximation, which enables us to compare the theory with numerical simulations. The fundamental soliton width, an invariant property of the quantum dark soliton, is shown to deviate from the Gross-Pitaevskii predictions in the interacting regime and vanishes in the Tonks-Girardeau limit.

cond-mat.quant-gas↗