184 research outputs found
One-dimensional two-component fermions with contact even-wave repulsion and SU(2) breaking near-resonant odd-wave attraction
We consider a one-dimensional (1D) two-component atomic Fermi gas with
contact interaction in the even-wave channel (Yang-Gaudin model) and study the
effect of an SU(2) symmetry breaking near-resonant odd-wave interaction within
one of the components. Starting from the microscopic Hamiltonian, we derive an
effective field theory for the spin degrees of freedom using the bosonization
technique. It is shown that at a critical value of the odd-wave interaction
there is a first-order phase transition from a phase with zero total spin and
zero magnetization to the spin-segregated phase where the magnetization locally
differs from zero.Comment: 18 pages, 3 fugures; references adde
Dynamical Quantum Hall Effect in the Parameter Space
Geometric phases in quantum mechanics play an extraordinary role in
broadening our understanding of fundamental significance of geometry in nature.
One of the best known examples is the Berry phase (M.V. Berry (1984), Proc.
Royal. Soc. London A, 392:45) which naturally emerges in quantum adiabatic
evolution. So far the applicability and measurements of the Berry phase were
mostly limited to systems of weakly interacting quasi-particles, where
interference experiments are feasible. Here we show how one can go beyond this
limitation and observe the Berry curvature and hence the Berry phase in generic
systems as a non-adiabatic response of physical observables to the rate of
change of an external parameter. These results can be interpreted as a
dynamical quantum Hall effect in a parameter space. The conventional quantum
Hall effect is a particular example of the general relation if one views the
electric field as a rate of change of the vector potential. We illustrate our
findings by analyzing the response of interacting spin chains to a rotating
magnetic field. We observe the quantization of this response, which term the
rotational quantum Hall effect.Comment: 7 pages, 5 figures added figure with anisotropic chai
Persistent currents in a multicomponent Tomonaga-Luttinger liquid: application to a mesoscopic semiconductor ring with spin-orbit interaction
The loschmidt index
We study the nodes of the wavefunction overlap between ground states of a parameterdependent Hamiltonian. These nodes are topological, and we can use them to analyze in a unifying way both equilibrium and dynamical quantum phase transitions in multiband systems. We define the Loschmidt index as the number of nodes in this overlap and discuss the relationship between this index and the wrapping number of a closed auxiliary hypersurface. This relationship allows us to compute this index systematically, using an integral representation of the wrapping number. We comment on the relationship between the Loschmidt index and other well-established topological numbers. As an example, we classify the equilibrium and dynamical quantum phase transitions of the XY model by counting the nodes in the wavefunction overlaps
The spectral form factor in the ‘t Hooft limit – Intermediacy versus universality
The Spectral Form Factor (SFF) is a convenient tool for the characterization
of eigenvalue statistics of systems with discrete spectra, and thus serves as a
proxy for quantum chaoticity. This work presents an analytical calculation of
the SFF of the Chern-Simons Matrix Model (CSMM), which was first introduced to
describe the intermediate level statistics of disordered electrons at the
mobility edge. The CSMM is characterized by a parameter ,
where the Circular Unitary Ensemble (CUE) is recovered for . The CSMM
was later found as a matrix model description of Chern-Simons theory on
, which is dual to a topological string theory characterized by string
coupling . The spectral form factor is proportional to a colored
HOMFLY invariant of a -torus link with its two components carrying the
fundamental and antifundamental representations, respectively. We check that
taking whilst keeping reduces the connected SFF to an
exact linear ramp of unit slope, confirming the main result from
arXiv:2012.11703 for the specific case of the CSMM. We then consider the `t
Hooft limit, where and such that remains
finite. As we take , this constitutes the opposite extreme of the CUE
limit. In the `t Hooft limit, the connected SFF turns into a remarkable
sequence of polynomials which, as far as the authors are aware, have not
appeared in the literature thus far. A gap opens in the spectrum and, after
unfolding by a constant rescaling, the connected SFF approximates a linear ramp
of unit slope for all except , where the connected SFF goes to
zero. We thus find that, although the CSMM was introduced to describe
intermediate statistics and the `t Hooft limit is the opposite limit of the
CUE, we still recover Wigner-Dyson universality for all except .Comment: Changes: 1. Added a treatment of unfolding and revised our
conclusions, changed title, abstract, introduction, and conclusion. 2.
Removed comparison with linear fit to connected SFF 3. Changed commas to
decimal points 4. Added figures on level density and unfolded SFF 5. Added
references 6. Corrected typos 30 pages, 6 figure
Preparation and detection of magnetic quantum phases in optical superlattices
We describe a novel approach to prepare, detect and characterize magnetic
quantum phases in ultra-cold spinor atoms loaded in optical superlattices. Our
technique makes use of singlet-triplet spin manipulations in an array of
isolated double well potentials in analogy to recently demonstrated quantum
control in semiconductor quantum dots. We also discuss the many-body
singlet-triplet spin dynamics arising from coherent coupling between nearest
neighbor double wells and derive an effective description for such system. We
use it to study the generation of complex magnetic states by adiabatic and
non-equilibrium dynamics.Comment: 5 pages, 2 Figures, reference adde
Interferometric probe of paired states
We propose a new method for detecting paired states in either bosonic or
fermionic systems using interference experiments with independent or weakly
coupled low dimensional systems. We demonstrate that our method can be used to
detect both the FFLO and the d-wave paired states of fermions, as well as
quasicondensates of singlet pairs for polar F=1 atoms in two dimensional
systems. We discuss how this method can be used to perform phase-sensitive
determination of the symmetry of the pairing amplitude.Comment: 17 pages, 5 figure
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