arXiv subjects

C. J. Bradly

Publications and source records attributed to C. J. Bradly.

12 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

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↗

arXiv2023

Critical behaviour of the extended-ballistic transition for pulled self-avoiding walks

In order to study long chain polymers many lattice models accommodate a pulling force applied to a particular part of the chain, often a free endpoint. This is in addition to well-studied features such as energetic interaction between the lattice polymer and a surface. However, the critical behaviour of the pulling force alone is less well studied, such as characterizing the nature of the phase transition and particularly the values of the associated exponents. We investigate a simple model of lattice polymers subject to forced extension, namely self-avoiding walks (SAWs) on the square and simple cubic lattices with one endpoint attached to an impermeable surface and a force applied to the other endpoint acting perpendicular to the surface. In the thermodynamic limit the system undergoes a transition to a ballistic phase as the force is varied and it is known that this transition occurs whenever the magnitude of the force is positive, i.e. $f>f_\text{c}=0$. Using well established scaling arguments we show that the crossover exponent $ϕ$ for the finite-size model is identical to the well-known exponent $ν_d$, which controls the scaling of the size of the polymer in $d$-dimensions. With extensive Monte Carlo simulations we test this conjecture and show that the value of $ϕ$ is indeed consistent with the known values of $ν_2 = 3/4$ and $ν_3 = 0.587 597(7)$. Scaling arguments, in turn, imply the specific heat exponent $α$ is $2/3$ in two dimensions and $0.29815(2)$ in three dimensions.

cond-mat.stat-mech↗

arXiv2022

Critical scaling of lattice polymers confined to a box without endpoint restriction

We study self-avoiding walks on the square lattice restricted to a square box of side $L$ weighted by a length fugacity without restriction of their end points. This models a confined polymer in dilute solution. The model admits a phase transition between an `empty' phase, where the average length of walks are finite and the density inside large boxes goes to zero, to a `dense' phase, where there is a finite positive density. We prove various bounds on the free energy and develop a scaling theory for the phase transition based on the standard theory for unconstrained polymers. We compare this model to unrestricted walks and walks that whose endpoints are fixed at the opposite corners of a box, as well as Hamiltonian walks. We use Monte Carlo simulations to verify predicted values for three key exponents: the density exponent $α=1/2$, the finite size crossover exponent $1/ν=4/3$ and the critical partition function exponent $2-η=43/24$. This implies that the theoretical framework relating them to the unconstrained SAW problem is valid.

cond-mat.stat-mech↗

arXiv2021

Polymer collapse of a self-avoiding trail model on a two-dimensional inhomogeneous lattice

The study of the effect of random impurities on the collapse of a flexible polymer in dilute solution has had recent attention with consideration of semi-stiff interacting self-avoiding walks on the square lattice. In the absence of impurities the model displays two types of collapsed phase, one of which is both anisotropically ordered and maximally dense (crystal-like). In the presence of impurities the study showed that the crystal type phase disappears. Here we investigate extended interacting self-avoiding trails on the triangular lattice with random impurities. Without impurities this model also displays two collapsed phases, one of which is maximally dense. However, this maximally dense phase is not ordered anisotropically. The trails are simulated using the flatPERM algorithm and the inhomogeneity is realised as a random fraction of the lattice that is unavailable to the trails. We calculate several thermodynamic and metric quantities to map out the phase diagram and look at how the amount of disorder affects the properties of each phase but especially the maximally dense phase. Our results indicate that while the maximally dense phase in the trail model is affected less than in the walk model it is also disrupted and becomes a denser version of the globule phase so that the model with impurities only displays no more than one true thermodynamic collapsed phase.

cond-mat.stat-mech↗

arXiv2018

Adsorption of neighbor-avoiding walks on the simple cubic lattice

We investigate neighbor-avoiding walks on the simple cubic lattice in the presence of an adsorbing surface. This class of lattice paths has been less studied using Monte Carlo simulations. Our investigation follows on from our previous results using self-avoiding walks and self-avoiding trails. The connection is that neighbor-avoiding walks are equivalent to the infinitely repulsive limit of self-avoiding walks with monomer-monomer interactions. Such repulsive interactions can be seen to enhance the excluded volume effect. We calculate the critical behavior of the adsorption transition for neighbor-avoiding walks, finding a critical temperature $T_{\text a}=3.274(9)$ and a crossover exponent $ϕ=0.482(13)$, which is consistent with the exponent for self-avoiding walks and trails, leading to an overall combined estimate for three dimensions of $ϕ_\text{3D}=0.484(7)$. While questions of universality have previously been raised regarding the value of adsorption exponents in three dimensions, our results indicate that the value of $ϕ$ in the strongly repulsive regime does not differ from its non-interacting value. However, it is clearly different from the mean-field value of $1/2$ and therefore not super-universal.

cond-mat.stat-mech↗

arXiv2017

Universality of crossover scaling for the adsorption transition of lattice polymers

Recently, it has been proposed that the adsorption transition for a single polymer in dilute solution, modeled by lattice walks in three dimensions, is not universal with respect to inter-monomer interactions. It has also been conjectured that key critical exponents $ϕ$, measuring the growth of the contacts with the surface at the adsorption point, and $1/δ$, which measures the finite-size shift of the critical temperature, are not the same. However, applying standard scaling arguments the two key critical exponents should be identical, thus pointing to a potential breakdown of these standard scaling arguments. This is in contrast to the well studied situation in two dimensions, where there are exact results from conformal field theory: these exponents are both accepted to be $1/2$ and universal. We use the flatPERM algorithm to simulate self-avoiding walks and trails on the hexagonal, square and simple cubic lattices up to length $1024$ to investigate these claims. Walks can be seen as a repulsive limit of inter-monomer interaction for trails, allowing us to probe the universality of adsorption. For each model we analyze several thermodynamic properties to produce different methods of estimating the critical temperature and the key exponents. We test our methodology on the two-dimensional cases and the resulting spread in values for $ϕ$ and $1/δ$ indicates that there is a systematic error that exceeds the statistical error usually reported. We further suggest a methodology for consistent estimation of the key adsorption exponents which gives $ϕ=1/δ=0.484(4)$ in three dimensions. We conclude that in three dimensions these critical exponents indeed differ from the mean-field value of $1/2$, but cannot find evidence that they differ from each other. Importantly, we also find no substantive evidence of any non-universality in the polymer adsorption transition.

cond-mat.stat-mech↗

arXiv2015

Analysis of two and three dipolar bosons in a spherical harmonic trap

As dipolar gases become more readily accessible in experiment there is a need to develop a comprehensive theoretical framework of the few-body physics of these systems. Here, we extend the coupled-pair approach developed for the unitary two-component Fermi gas to a few-body system of dipolar bosons in a spherical harmonic trap. The long range and anisotropy of the dipole-dipole interaction is handled by a flexible and efficient correlated gaussian basis with stochastically variational optimisation. We calculate the eigenenergy spectrum and structural properties of two and three trapped bosonic dipoles. This demonstrates the efficiency and flexibility of the coupled-pair approach at dealing with systems with complex interactions.

cond-mat.quant-gas↗

arXiv2014

Coupled pair approach for strongly-interacting trapped fermionic atoms

We present a coupled pair approach for studying few-body physics in harmonically trapped ultracold gases. The method is applied to a two-component Fermi system of $N$ particles. A stochastically variational gaussian expansion method is applied, focusing on optimization of the two-body correlations present in the strongly interacting, or unitary, limit. The groundstate energy of the four-, six- and eight-body problem with equal spin populations is calculated with high accuracy and minimal computational effort. We also calculate the structural properties of these systems and discuss their implication for the many-body ultracold gas and other few-body calculations.

cond-mat.quant-gas↗

arXiv2012

Universality and itinerant ferromagnetism in rotating strongly interacting Fermi gases

We analytically determine the properties of three interacting fermions in a harmonic trap subject to an external rotation. Thermodynamic quantities such as the entropy and energy are calculated from the third order quantum virial expansion. By parameterizing the solutions in the rotating frame we find that the energy and entropy are universal for all rotations in the strongly interacting regime. Additionally, we find that rotation suppresses the onset of itinerant ferromagnetism in strongly interacting repulsive three-body systems.

cond-mat.quant-gas↗

arXiv2012

Universality in rotating strongly interacting gases

We analytically determine the properties of two interacting particles in a harmonic trap subject to a rotation or a uniform synthetic magnetic field, where the spherical symmetry of the relative Hamiltonian is preserved. Thermodynamic quantities such as the entropy and energy are calculated via the second order quantum cluster expansion. We find that in the strongly interacting regime the energy is universal, however the entropy changes as a function of the rotation or synthetic magnetic field strength.

cond-mat.quant-gas↗

arXiv2012

Coherent tunneling via adiabatic passage in a three-well Bose-Hubbard system

We apply the Bose-Hubbard Hamiltonian to a three-well system and show analytically that coherent transport via adiabatic passage (CTAP) of $N$ non-interacting particles across the chain is possible. We investigate the effect of detuning the middle well to recover CTAP when on-site interparticle interactions would otherwise disrupt the transport. The case of small interactions is restated using first-order perturbation theory to develop criteria for adibaticity that define the regime where CTAP is possible. Within this regime we investigate restricting the Hilbert space to the minimum necessary basis needed to demonstrate CTAP, which dramatically increases the number of particles that can be efficiently considered. Finally, we compare the results of the Bose-Hubbard model to a mean-field three-mode Gross-Pitaevskii analysis for the equivalent system.

cond-mat.quant-gas↗