66 research outputs found
Variational Schrieffer-Wolff transformations for quantum many-body dynamics
Building on recent results for adiabatic gauge potentials, we propose a variational approach for computing the generator of Schrieffer-Wolff transformations. These transformations consist of block diagonalizing a Hamiltonian through a unitary rotation, which leads to effective dynamics in a computationally tractable reduced Hilbert space. The generators of these rotations are computed variationally and thus go beyond standard perturbative methods, with error controlled by the locality of the variational ansatz. The method is demonstrated on two models. First, in the attractive Fermi-Hubbard model with onsite disorder, we find indications of a lack of observable many-body localization in the thermodynamic limit due to the inevitable mixture of different spinon sectors. Second, in the low-energy sector of the XY spin model with a broken U(1) symmetry, we analyze ground-state response functions by combining the variational Schrieffer-Wolf transformation with the truncated spectrum approach.Published versio
Read-Green resonances in a topological superconductor coupled to a bath
We study a topological superconductor capable of exchanging particles with an
environment. This additional interaction breaks particle-number symmetry and
can be modelled by means of an integrable Hamiltonian, building on the class of
Richardson-Gaudin pairing models. The isolated system supports zero-energy
modes at a topological phase transition, which disappear when allowing for
particle exchange with an environment. However, it is shown from the exact
solution that these still play an important role in system-environment particle
exchange, which can be observed through resonances in low-energy and -momentum
level occupations. These fluctuations signal topologically protected Read-Green
points and cannot be observed within traditional mean-field theory.Comment: 7 pages, 4 figure
Floquet-engineering counterdiabatic protocols in quantum many-body systems
Counterdiabatic (CD) driving presents a way of generating adiabatic dynamics
at arbitrary pace, where excitations due to non-adiabaticity are exactly
compensated by adding an auxiliary driving term to the Hamiltonian. While this
CD term is theoretically known and given by the adiabatic gauge potential,
obtaining and implementing this potential in many-body systems is a formidable
task, requiring knowledge of the spectral properties of the instantaneous
Hamiltonians and control of highly nonlocal multibody interactions. We show how
an approximate gauge potential can be systematically built up as a series of
nested commutators, remaining well-defined in the thermodynamic limit.
Furthermore, the resulting CD driving protocols can be realized up to arbitrary
order without leaving the available control space using tools from
periodically-driven (Floquet) systems. This is illustrated on few- and
many-body quantum systems, where the resulting Floquet protocols significantly
suppress dissipation and provide a drastic increase in fidelity.Comment: 6+3 page
Inner products in integrable Richardson-Gaudin models
We present the inner products of eigenstates in integrable Richardson-Gaudin
models from two different perspectives and derive two classes of Gaudin-like
determinant expressions for such inner products. The requirement that one of
the states is on-shell arises naturally by demanding that a state has a dual
representation. By implicitly combining these different representations, inner
products can be recast as domain wall boundary partition functions. The
structure of all involved matrices in terms of Cauchy matrices is made explicit
and used to show how one of the classes returns the Slavnov determinant
formula. This framework provides a further connection between two different
approaches for integrable models, one in which everything is expressed in terms
of rapidities satisfying Bethe equations, and one in which everything is
expressed in terms of the eigenvalues of conserved charges, satisfying
quadratic equations.Comment: 21+16 pages, minor revisions compared to the previous versio
Integrable spin-1/2 Richardson-Gaudin XYZ models in an arbitrary magnetic field
We establish the most general class of spin-1/2 integrable Richardson-Gaudin
models including an arbitrary magnetic field, returning a fully anisotropic
(XYZ) model. The restriction to spin-1/2 relaxes the usual integrability
constraints, allowing for a general solution where the couplings between spins
lack the usual antisymmetric properties of Richardson-Gaudin models. The full
set of conserved charges are constructed explicitly and shown to satisfy a set
of quadratic equations, allowing for the numerical treatment of a fully
anisotropic central spin in an external magnetic field. While this approach
does not provide expressions for the exact eigenstates, it allows their
eigenvalues to be obtained, and expectation values of local observables can
then be calculated from the Hellmann-Feynman theorem.Comment: 11 pages, 1 figur
Integrability and duality in spin chains
We construct a new, two-parametric family of integrable models and reveal
their underlying duality symmetry. A modular subgroup of this duality is shown
to connect non-interacting modes of different systems. We apply the new
solution and duality to a Richardson-Gaudin model and generate a novel
integrable system termed the - wave Richardson-Gaudin-Kitaev interacting
chain, interpolating - and - wave superconductivity. The phase diagram of
this model has a topological phase transition that can be connected to the
duality, where the occupancy of the non-interacting mode serves as a
topological order parameter.Comment: 10 pages, 2 figures, typos added, reference added, footnote [58]
added on page 2, changed phrasing on YBE, acknowledgements update
An eigenvalue-based method and determinant representations for general integrable XXZ Richardson-Gaudin models
We propose an extension of the numerical approach for integrable
Richardson-Gaudin models based on a new set of eigenvalue-based variables.
Starting solely from the Gaudin algebra, the approach is generalized towards
the full class of XXZ Richardson-Gaudin models. This allows for a fast and
robust numerical determination of the spectral properties of these models,
avoiding the singularities usually arising at the so-called singular points. We
also provide different determinant expressions for the normalization of the
Bethe Ansatz states and form factors of local spin operators, opening up
possibilities for the study of larger systems, both integrable and
non-integrable. These expressions can be written in terms of the new set of
variables and generalize the results previously obtained for rational
Richardson-Gaudin models and Dicke-Jaynes-Cummings-Gaudin models. Remarkably,
these results are independent of the explicit parametrization of the Gaudin
algebra, exposing a universality in the properties of Richardson-Gaudin
integrable systems deeply linked to the underlying algebraic structure
Spin polarization through Floquet resonances in a driven central spin model
Adiabatically varying the driving frequency of a periodically-driven
many-body quantum system can induce controlled transitions between resonant
eigenstates of the time-averaged Hamiltonian, corresponding to adiabatic
transitions in the Floquet spectrum and presenting a general tool in quantum
many-body control. Using the central spin model as an application, we show how
such controlled driving processes can lead to a polarization-based decoupling
of the central spin from its decoherence-inducing environment at resonance.
While it is generally impossible to obtain the exact Floquet Hamiltonian in
driven interacting systems, we exploit the integrability of the central spin
model to show how techniques from quantum quenches can be used to explicitly
construct the Floquet Hamiltonian in a restricted many-body basis and model
Floquet resonances.Comment: 6+4 page
- …