arXiv subjects

Ryan Barnett

Publications and source records attributed to Ryan Barnett.

At least 19 recordsLinked to original sources

arXiv2025

Microscopic theory of Chern polarization via crystalline defect charge

The modern theory of polarization does not apply in its original form to systems with non-trivial band topology. Chern insulators are one such example. Defining polarization for them is complicated because they are insulating in the bulk but exhibit metallic edge states. Wannier functions formed a key ingredient of the original modern theory of polarization, but it has been considered that these cannot be applied to Chern insulators since they are no longer exponentially localized and the Wannier center, obtained from the Zak phase, is no longer gauge invariant. In this article, we provide an unambiguous definition of absolute polarization for a Chern insulator in terms of the Zak phase. We obtain our expression by studying the non-quantized fractional charge bound to lattice dislocations. Our expression can be computed directly from bulk quantities and makes no assumption on the edge state filling. It is fully consistent with previous results on the quantized charge bound to dislocations in the presence of crystalline symmetry. At the same time, our result is more general since it also applies to Chern insulators which do not have crystalline symmetries other than translations.

cond-mat.str-el↗

arXiv2024

Unvortex Lattice and Topological Defects in Rigidly Rotating Multicomponent Superfluids

By examining rotating ferromagnetic spinor condensates through the perspective of large spin, we identify a novel type of topological point defects in the magnetization texture. These defects are not predicted by conventional homotopy analysis but rather by the Riemann-Hurwitz formula. The magnetization texture in the system is described by an equal-area mapping from the plane to the sphere of magnetization, forming a lattice of uniformly charged Skyrmions. This lattice contains doubly-quantized (winding number = 2) point defects arranged on the sphere in a tetrahedral configuration. The fluid found to be rotating rigidly, except at the point defects, where the vorticity vanishes. This vorticity structure describes an unconventional "unvortex" lattice, which contrasts with the well-known vortex lattice in scalar rotating superfluids, where vorticity is concentrated exclusively within defect points. Numerical results are presented, confirming these predictions and demonstrating their persistence in smaller-spin condensates.

cond-mat.quant-gas↗

arXiv2023

Optimally Localized Wannier Functions for 2D Chern Insulators

The construction of optimally localized Wannier functions (and Wannier functions in general) for a Chern insulator has been considered to be impossible owing to the fact that the second moment of such functions is generally infinite. In this manuscript, we propose a solution to this problem in the case of a single band. We accomplish this by drawing an analogy between the minimization of the variance and the minimization of the electrostatic energy of a periodic array of point charges in a smooth neutralizing background. In doing so, we obtain a natural regularization of the diverging variance and this leads to an analytical solution to the minimization problem. We demonstrate our results numerically for a particular model system. Furthermore, we show how the optimally localized Wannier functions provide a natural way of evaluating the electric polarization for a Chern insulator.

cond-mat.mtrl-sci↗

arXiv2022

Quantised Bulk Conductivity as a Local Chern Marker

A central property of Chern insulators is the robustness of the topological phase and edge states to impurities in the system. Despite this, Chern number cannot be straightforwardly calculated in the presence of disorder. Recently, work has been done to propose a local analog of the Chern number, called local markers, that can be used to characterise disordered systems. However, it was unclear whether the proposed markers represented a physically-measurable property of the system. Here we propose a local marker starting from a physical argument, as a local cross-conductivity measured in the bulk of the system. We find the explicit form of the marker for a non-interacting system of electrons on the lattice and show that it corresponds to existing expressions for the Chern number. Examples are calculated for a variety of disordered and amorphous systems, showing that it is precisely quantised to the Chern number and robust against disorder.

cond-mat.str-el↗

arXiv2022

1D quasicrystals and topological markers

Local topological markers are effective tools for determining the topological properties of both homogeneous and inhomogeneous systems. The Chern marker is an established topological marker that has previously been shown to effectively reveal the topological properties of 2D systems. In an earlier work, the present authors have developed a marker that can be applied to 1D time-dependent systems which can be used to explore their topological properties, like charge pumping under the presence of disorder. In this paper, we show how to alter the 1D marker so that it can be applied to quasiperiodic and aperiodic systems. We then verify its effectiveness against different quasicrystal Hamiltonians, some which have been addressed in previous studies using existing methods, and others which possess topological structures that have been largely unexplored. We also demonstrate that the altered 1D marker can be productively applied to systems that are fully aperiodic.

cond-mat.quant-gas↗

arXiv2021

The effect of boson-boson interaction on the Bipolaron formation

Impurities immersed into a surrounding ultra-cold Bose gas experience interactions mediated by the surrounding many-body environment. If one focuses on two impurities that are sufficiently close to each other, they can form a bipolaron pair. Here, we discuss how the standard methods based on linearizing the condensate field lead to results only valid in the weak coupling regime and for sufficiently large impurity separations. We show how those shortcomings can be remedied within the Born-Oppenheimer approximation by accounting for boson-boson interactions already on the mean-field level.

cond-mat.quant-gas↗

arXiv2021

Stochastic-field approach to the quench dynamics of the one-dimensional Bose polaron

We consider the dynamics of a quantum impurity after a sudden interaction quench into a one-dimensional degenerate Bose gas. We use the Keldysh path integral formalism to derive a truncated Wigner like approach that takes the back action of the impurity onto the condensate into account already on the mean-field level and further incorporates thermal and quantum effects up to one-loop accuracy. This framework enables us not only to calculate the real space trajectory of the impurity but also the absorption spectrum. We find that quantum corrections and thermal effects play a crucial role for the impurity momentum at weak to intermediate impurity-bath couplings.Furthermore, we see the broadening of the absorption spectrum with increasing temperature.

cond-mat.quant-gas↗

arXiv2020

Local Topological Markers in Odd Dimensions

Local topological markers have proven to be a valuable tool for investigating systems with topologically non-trivial bands. Due to their local nature, such markers can treat translationally invariant systems and spatially inhomogeneous systems on an equal footing. Among the most prevalent of these is the so-called Chern marker, which is available for systems in two spatial dimensions. In this paper, we describe how to generalize this marker to 1d and 3d systems, by showing that the relevant expressions accurately describe the phenomenon of topological pumping given by the first and second Chern numbers in 1d and 3d respectively. In addition to providing general derivations, we verify the markers by numerically considering model Hamiltonians. These results will open the door for future studies including the influence of disorder on topological pumping and topological phase transitions in odd-dimensional systems.

cond-mat.quant-gas↗

arXiv2019

Strong-coupling Bose polarons in 1D: Condensate deformation and modified Bogoliubov phonons

We discuss the interaction of a quantum impurity with a one-dimensional degenerate Bose gas forming a Bose-polaron. In three spatial dimensions the quasiparticle is typically well described by the extended Fr\"ohlich model, in full analogy with the solid-state counterpart. This description, which assumes an undepleted condensate, fails however in 1D, where the backaction of the impurity on the condensate leads to a self-bound mean-field polaron for arbitrarily weak impurity-boson interactions. We present a model that takes into account this backaction and describes the impurity-condensate interaction as coupling to phonon-like excitations of a deformed condensate. A comparison of polaron energies and masses to diffusion quantum Monte-Carlo simulations shows very good agreement already on the level of analytical mean-field solutions and is further improved when taking into account quantum fluctuations.

cond-mat.quant-gas↗

arXiv2019

Exotic Vortex Lattices in Binary Repulsive Superfluids

We investigate a mixture of two repulsively interacting superfluids with different constituent particle masses: $m_1\ne m_2$. Solutions to the Gross-Pitaevskii equation for homogeneous infinite vortex lattices predict the existence of rich vortex lattice configurations, a number of which correspond to Platonic and Archimedean planar tilings. Some notable geometries include the snub-square, honeycomb, kagome, and herringbone lattice configurations. We present a full phase diagram for the case $m_2/m_1 = 2$ and list a number of geometries that are found for higher integer mass ratios.

cond-mat.quant-gas↗

arXiv2017

Vortex Lattices in Binary Mixtures of Repulsive Superfluids

We present an extension of the framework introduced in [1] to treat multicomponent systems, showing that new degrees of freedom are necessary in order to obtain the desired boundary conditions. We then apply this extended framework to the coupled Gross-Pitaevskii equations to investigate the ground states of two-component systems with equal masses thereby extending previous work in the lowest Landau limit [2] to arbitrary interactions within Gross-Pitaevskii theory. We show that away from the lowest-Landau level limit, the predominant vortex lattice consists of two interlaced triangular lattices. Finally, we derive a linear relation which accurately describes the phase boundaries in the strong interacting regimes.

cond-mat.quant-gas↗

arXiv2017

Topological Edge-State Manifestation of Interacting 2D Condensed Boson-Lattice Systems in a Harmonic Trap

In this Letter, it is shown that interactions can facilitate the emergence of topological edge states of quantum-degenerate bosonic systems in the presence of a harmonic potential. This effect is demonstrated with the concrete model of a hexagonal lattice populated by spin-one bosons under a synthetic gauge field. In fermionic or noninteracting systems, the presence of a harmonic trap can obscure the observation of edge states. For our system with weakly interacting bosons in the Thomas--Fermi regime, we can clearly see a topological band structure with a band gap traversed by edge states. We also find that the number of edge states crossing the gap is increased in the presence of a harmonic trap, and the edge modes experience an energy shift while traversing the first Brillouin zone which is related to the topological properties of the system. We find an analytical expression for the edge-state energies and our comparison with numerical computation shows excellent agreement.

cond-mat.quant-gas↗

arXiv2017

Frustration-free Hamiltonians supporting Majorana zero edge modes

A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs.

quant-ph↗

arXiv2016

Quantum Rotor Theory of Systems of Spin-2 Bosons

We consider quantum phases of tightly-confined spin-2 bosons in an external field under the presence of rotationally-invariant interactions. Generalizing previous treatments, we show how this system can be mapped onto a quantum rotor model. Within the rotor framework, low-energy excitations about fragmented states, which cannot be accessed within standard Bogoliubov theory, can be obtained. In the spatially extended system in the thermodynamic limit there exists a mean-field ground state degeneracy between a family of nematic states for appropriate interaction parameters. It has been established that quantum fluctuations lift this degeneracy through the mechanism of order-by-disorder and select either a uniaxial or square-biaxial ground state. On the other hand, in the full quantum treatment of the analogous single-spatial mode problem with finite particle number it is known that, due to symmetry restoring fluctuations, there is a unique ground state across the entire nematic region of the phase diagram. Within the established rotor framework we investigate the possible quantum phases under the presence of a quadratic Zeeman field, a problem which has previously received little attention. By investigating wave function overlaps we do not find any signatures of the order-by-disorder phenomenon which is present in the continuum case. Motivated by this we consider an alternative external potential which breaks less symmetry than the quadratic Zeeman field. For this case we do find the phenomenon of order-by-disorder in the fully quantum system. This is established within the rotor framework and with exact diagonalization.

cond-mat.quant-gas↗

arXiv2016

Simulating Infinite Vortex Lattices in Superfluids

We present an efficient framework to numerically treat infinite periodic vortex lattices in rotating superfluids described by the Gross-Pitaevskii theory. The commonly used split-step Fourier (SSF) spectral methods are inapplicable to such systems as the standard Fourier transform does not respect the boundary conditions mandated by the magnetic translation group. We present a generalisation of the SSF method which incorporates the correct boundary conditions by employing the so-called magnetic Fourier transform. We test the method and show that it reduces to known results in the lowest-Landau-level regime. While we focus on rotating scalar superfluids for simplicity, the framework can be naturally extended to treat multicomponent systems and systems under more general `synthetic' gauge fields.

cond-mat.quant-gas↗

arXiv2015

Selective Population of Edge States in a 2D Topological Band System

We consider a system of interacting spin-one atoms in a hexagonal lattice under the presence of a synthetic gauge field. Quenching the quadratic Zeeman field is shown to lead to a dynamical instability of the edge modes. This, in turn, leads to a spin current along the boundary of the system which grows exponentially fast in time following the quench. Tuning the magnitude of the quench can be used to selectively populate edge modes of different momenta. Implications of the intrinsic symmetries of Hamiltonian on the dynamics are discussed. The results hold for atoms with both antiferromagnetic and ferromagnetic interactions.

cond-mat.quant-gas↗

arXiv2014

Order-by-Disorder Degeneracy Lifting of Interacting Bosons on the Dice Lattice

Motivated by recent experimental progress in the realization of synthetic gauge fields in systems of ultracold atoms, we consider interacting bosons on the dice lattice with half flux per plaquette. All bands of the non-interacting spectrum of this system were previously found to have the remarkable property of being completely dispersionless. We show that degeneracies remain when interactions are treated at the level of mean field theory, and the ground state exhibits vortex lattice configurations already established in the simpler XY model in the same geometry. We argue that including quantum and thermal fluctuations will select a unique vortex lattice up to overall symmetries based on the order-by-disorder mechanism. We verify the stability of the selected state by analyzing the condensate depletion. The latter is shown to exhibit an unusual non-monotonic behavior as a function of the interaction parameters which can be understood as a consequence of the dispersionless nature of the non-interacting spectrum. Finally, we comment on the role of domain walls which have interactions mediated through fluctuations.

cond-mat.quant-gas↗

arXiv2014

Edge-state instabilities of bosons in a topological band

In this work, we consider the dynamics of bosons in bands with non-trivial topological structure. In particular, we focus on the case where bosons are prepared in a higher-energy band and allowed to evolve. The Bogoliubov theory about the initial state can have a dynamical instability, and we show that it is possible to achieve the interesting situation where the topological edge modes are unstable while all bulk modes are stable. Thus, after the initial preparation, the edge modes will become rapidly populated. We illustrate this with the Su-Schrieffer-Heeger model which can be realized with a double-well optical lattice and is perhaps the simplest model with topological edge states. This work provides a direct physical consequence of topological bands whose properties are often not of immediate relevance for bosonic systems.

cond-mat.quant-gas↗