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Jon Links

Publications and source records attributed to Jon Links.

At least 55 records · Page 3Linked to original sources
arXiv2009

Universal construction of order parameters for translation-invariant quantum lattice systems with symmetry-breaking order

For any translation-invariant quantum lattice system with a symmetry group G, we propose a practical and universal construction of order parameters which identify quantum phase transitions with symmetry-breaking order. They are defined in terms of the fidelity between a ground state and its symmetry-transformed counterpart, and are computed through tensor network representations of the ground-state wavefunction. To illustrate our scheme, we consider three quantum systems on an infinite lattice in one spatial dimension, namely, the quantum Ising model in a transverse magnetic field, the quantum spin-1/2 XYX model in an external magnetic field, and the quantum spin-1 XXZ model with single-ion anisotropy. All these models have symmetry group Z_2 and exhibit broken-symmetry phases. We also discuss the role of the order parameters in identifying factorized states.

cond-mat.stat-mech↗
arXiv2009

Exactly solvable pairing model for superconductors with a p+ip-wave symmetry

We present the exact Bethe ansatz solution for the two-dimensional BCS pairing Hamiltonian with p_x + i p_y symmetry. Using both mean-field theory and the exact solution we obtain the ground-state phase diagram parameterized by the filling fraction and the coupling constant. It consists of three phases denoted weak coupling BCS, weak pairing, and strong pairing. The first two phases are separated by a topologically protected line where the exact ground state is given by the Moore-Read pfaffian state. In the thermodynamic limit the ground-state energy is discontinuous on this line. The other two phases are separated by the critical line, also topologically protected, previously found by Read and Green. We establish a duality relation between the weak and strong pairing phases, whereby ground states of the weak phase are "dressed" versions of the ground states of the strong phase by zero energy (Moore-Read) pairs and characterized by a topological order parameter.

cond-mat.supr-con↗
arXiv2007

Ground-state properties of the attractive one-dimensional Bose-Hubbard model

We study the ground state of the attractive one-dimensional Bose-Hubbard model, and in particular the nature of the crossover between the weak interaction and strong interaction regimes for finite system sizes. Indicator properties like the gap between the ground and first excited energy levels, and the incremental ground-state wavefunction overlaps are used to locate different regimes. Using mean-field theory we predict that there are two distinct crossovers connected to spontaneous symmetry breaking of the ground state. The first crossover arises in an analysis valid for large L with finite N, where L is the number of lattice sites and N is the total particle number. An alternative approach valid for large N with finite L yields a second crossover. For small system sizes we numerically investigate the model and observe that there are signatures of both crossovers. We compare with exact results from Bethe ansatz methods in several limiting cases to explore the validity for these numerical and mean-field schemes. The results indicate that for finite attractive systems there are generically three ground-state phases of the model.

cond-mat.stat-mech↗
arXiv2006

Bethe Ansatz Solutions of the Bose-Hubbard Dimer

The Bose-Hubbard dimer Hamiltonian is a simple yet effective model for describing tunneling phenomena of Bose-Einstein condensates. One of the significant mathematical properties of the model is that it can be exactly solved by Bethe ansatz methods. Here we review the known exact solutions, highlighting the contributions of V.B. Kuznetsov to this field. Two of the exact solutions arise in the context of the Quantum Inverse Scattering Method, while the third solution uses a differential operator realisation of the su(2) Lie algebra.

nlin.SI↗
arXiv2006

On quantum phase crossovers in finite systems

In this work we define a formal notion of a quantum phase crossover for certain Bethe ansatz solvable models. The approach we adopt exploits an exact mapping of the spectrum of a many-body integrable system, which admits an exact Bethe ansatz solution, into the quasi-exactly solvable spectrum of a one-body Schrödinger operator. Bifurcations of the minima for the potential of the Schrödinger operator determine the crossover couplings. By considering the behaviour of particular ground-state correlation functions, these may be identified as quantum phase crossovers in the many-body integrable system with finite particle number. In this approach the existence of the quantum phase crossover is not dependent on the existence of a thermodynamic limit, rendering applications to finite systems feasible. We study two examples of bosonic Hamiltonians which admit second-order crossovers.

quant-ph↗
arXiv2006

Emergent quantum phases in a heteronuclear molecular Bose--Einstein condensate model

We study a three-mode Hamiltonian modelling a heteronuclear molecular Bose--Einstein condensate. Two modes are associated with two distinguishable atomic constituents, which can combine to form a molecule represented by the third mode. Beginning with a semi-classical analogue of the model, we conduct an analysis to determine the phase space fixed points of the system. Bifurcations of the fixed points naturally separate the coupling parameter space into different regions. Two distinct scenarios are found, dependent on whether the imbalance between the number operators for the atomic modes is zero or non-zero. This result suggests the ground-state properties of the model exhibit an unusual sensitivity on the atomic imbalance. We then test this finding for the quantum mechanical model. Specifically we use Bethe ansatz methods, ground-state expectation values, the character of the quantum dynamics, and ground-state wavefunction overlaps to clarify the nature of the ground-state phases. The character of the transition is smoothed due to quantum fluctuations, but we may nonetheless identify the emergence of a quantum phase boundary in the limit of zero atomic imbalance.

quant-ph↗
arXiv2005

Teleportation via multi-qubit channels

We investigate the problem of teleporting an unknown qubit state to a recipient via a channel of $2Ł$ qubits. In this procedure a protocol is employed whereby $Ł$ Bell state measurements are made and information based on these measurements is sent via a classical channel to the recipient. Upon receiving this information the recipient determines a local gate which is used to recover the original state. We find that the $2^{2Ł}$-dimensional Hilbert space of states available for the channel admits a decomposition into four subspaces. Every state within a given subspace is a perfect channel, and each sequence of Bell measurements projects $2Ł$ qubits of the system into one of the four subspaces. As a result, only two bits of classical information need be sent to the recipient for them to determine the gate. We note some connections between these four subspaces and ground states of many-body Hamiltonian systems, and discuss the implications of these results towards understanding entanglement in multi-qubit systems.

quant-ph↗
arXiv2005

Infinitely many two-variable generalisations of the Alexander-Conway polynomial

We show that the Alexander-Conway polynomial Delta is obtainable via a particular one-variable reduction of each two-variable Links-Gould invariant LG^{m,1}, where m is a positive integer. Thus there exist infinitely many two-variable generalisations of Delta. This result is not obvious since in the reduction, the representation of the braid group generator used to define LG^{m,1} does not satisfy a second-order characteristic identity unless m=1. To demonstrate that the one-variable reduction of LG^{m,1} satisfies the defining skein relation of Delta, we evaluate the kernel of a quantum trace.

math.GT↗
arXiv2005

Where the Links--Gould invariant first fails to distinguish nonmutant prime knots

It is known that the first two-variable Links--Gould quantum link invariant $LG\equiv LG^{2,1}$ is more powerful than the HOMFLYPT and Kauffman polynomials, in that it distinguishes all prime knots (including reflections) of up to 10 crossings. Here we report investigations which greatly expand the set of evaluations of $LG$ for prime knots. Through them, we show that the invariant is complete, modulo mutation, for all prime knots (including reflections) of up to 11 crossings, but fails to distinguish some nonmutant pairs of 12-crossing prime knots. As a byproduct, we classify the mutants within the prime knots of 11 and 12 crossings. In parallel, we learn that $LG$ distinguishes the chirality of all chiral prime knots of at most 12 crossings. We then demonstrate that every mutation-insensitive link invariant fails to distinguish the chirality of a number of 14-crossing prime knots. This provides 14-crossing examples of chiral prime knots whose chirality is undistinguished by $LG$.

math.GT↗
arXiv2005

Quantifying ground state entanglement of the BCS model

The concept of local concurrence is used to quantify the entanglement between a single qubit and the remainder of a multi-qubit system. For the ground state of the BCS model in the thermodynamic limit the set of local concurrences completely describe the entanglement. As a measure for the entanglement of the full system we investigate the Average Local Concurrence (ALC). We find that the ALC satisfies a simple relation with the order parameter. We then show that for finite systems with fixed particle number, a relation between the ALC and the condensation energy exposes a threshold coupling. Below the threshold, entanglement measures besides the ALC are significant.

quant-ph↗
arXiv2005

Ribbon Structure in Symmetric Pre-monoidal Categories

Let U(g) denote the universal enveloping algebra of a Lie algebra g. We show the existence of a ribbon algebra in a particular deformation of U(g) which leads to a symmetric pre-monoidal category of U(g)-modules.

math.CT↗
arXiv2004

Energy level statistics for models of coupled single-mode Bose--Einstein condensates

We study the distribution of energy level spacings in two models describing coupled single-mode Bose-Einstein condensates. Both models have a fixed number of degrees of freedom, which is small compared to the number of interaction parameters, and is independent of the dimensionality of the Hilbert space. We find that the distribution follows a universal Poisson form independent of the choice of coupling parameters, which is indicative of the integrability of both models. These results complement those for integrable lattice models where the number of degrees of freedom increases with increasing dimensionality of the Hilbert space. Finally, we also show that for one model the inclusion of an additional interaction which breaks the integrability leads to a non-Poisson distribution.

quant-ph↗
arXiv2004

Integrability of the russian doll BCS model

We show that integrability of the BCS model extends beyond Richardson's model (where all Cooper pair scatterings have equal coupling) to that of the russian doll BCS model for which the couplings have a particular phase dependence that breaks time-reversal symmetry. This model is shown to be integrable using the quantum inverse scattering method, and the exact solution is obtained by means of the algebraic Bethe ansatz. The inverse problem of expressing local operators in terms of the global operators of the monodromy matrix is solved. This result is used to find a determinant formulation of a correlation function for fluctuations in the Cooper pair occupation numbers. These results are used to undertake exact numerical analysis for small systems at half-filling.

cond-mat.stat-mech↗
arXiv2002

Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate

We study the exact solution for a two-mode model describing coherent coupling between atomic and molecular Bose-Einstein condensates (BEC), in the context of the Bethe ansatz. By combining an asymptotic and numerical analysis, we identify the scaling behaviour of the model and determine the zero temperature expectation value for the coherence and average atomic occupation. The threshold coupling for production of the molecular BEC is identified as the point at which the energy gap is minimum. Our numerical results indicate a parity effect for the energy gap between ground and first excited state depending on whether the total atomic number is odd or even. The numerical calculations for the quantum dynamics reveals a smooth transition from the atomic to the molecular BEC.

cond-mat.stat-mech↗
arXiv2002

Integrability and exact solution for coupled BCS systems associated with the $su(4)$ Lie algebra

We introduce an integrable model for two coupled BCS systems through a solution of the Yang-Baxter equation associated with the Lie algebra $su(4)$. By employing the algebraic Bethe ansatz, we determine the exact solution for the energy spectrum. An asymptotic analysis is conducted to determine the leading terms in the ground state energy, the gap and some one point correlation functions at zero temperature.

cond-mat.str-el↗
arXiv2002

Exact results for a tunnel-coupled pair of trapped Bose-Einstein condensates

A model describing coherent quantum tunneling between two trapped Bose-Einstein condensates is shown to admit an exact solution. The spectrum is obtained by the algebraic Bethe ansatz. An asymptotic analysis of the Bethe ansatz equations leads us to explicit expressions for the energies of the ground and first excited states in the limit of {\it weak} tunneling and all energies for {\it strong} tunneling. The results are used to extract the asymptotic limits of the quantum fluctuations of the boson number difference between the two Bose-Einstein condensates and to characterize the degree of coherence in the system.

cond-mat.mes-hall↗
arXiv2001

Integrable Impurity Spin Ladder Systems

Two integrable spin ladder systems with different types of impurities are proposed. The impurities are introduced in such a way that the integrability of the models is not violated. The models are solved exactly and the Bethe ansatz equations as well as the energy eigenvalues are obtained. We show for both models that a phase transition between gapped and gapless spin excitations occurs at a critical value of the rung coupling J. In addition, the dependence of the impurities on this phase transition is determined explicitly. Remarkably, in one of the models a decreasing of the spin gap with increasing impurity strength is found.

cond-mat.stat-mech↗