71 research outputs found
The equilibrium landscape of the Heisenberg spin chain
We characterise the equilibrium landscape, the entire manifold of local
equilibrium states, of an interacting integrable quantum model. Focusing on the
isotropic Heisenberg spin chain, we describe in full generality two
complementary frameworks for addressing equilibrium ensembles: the functional
integral Thermodynamic Bethe Ansatz approach, and the lattice regularisation
transfer matrix approach. We demonstrate the equivalence between the two, and
in doing so clarify several subtle features of generic equilibrium states. In
particular we explain the breakdown of the canonical Y-system, which reflects a
hidden structure in the parametrisation of equilibrium ensembles.Comment: 31 pages, revised versio
Fermi surface enlargement on the Kondo lattice
The Kondo lattice model is a paradigmatic model for the description of local
moment systems, a class of materials exhibiting a range of strongly correlated
phenomena including heavy fermion formation, magnetism, quantum criticality and
unconventional superconductivity. Conventional theoretical approaches invoke
fractionalization of the local moment spin through large-N and slave particle
methods. In this work we develop a new formalism, based instead on
non-canonical degrees of freedom. We demonstrate that the graded Lie algebra
su(2|2) provides a powerful means of organizing correlations on the Kondo
lattice through a splitting of the electronic degree of freedom, in a manner
which entwines the conduction electrons with the local moment spins. This
offers a novel perspective on heavy fermion formation. Unlike slave-particle
methods, non-canonical degrees of freedom generically allow for a violation of
the Luttinger sum rule, and we interpret recent angle resolved photoemission
experiments on Ce-115 systems in view of this.Comment: 8 pages, 1 figur
Modulated trapping of interacting bosons in one dimension
We investigate the response of harmonically confined bosons with contact
interactions (trapped Lieb-Liniger gas) to modulations of the trapping
strength. We explain the structure of resonances at a series of driving
frequencies, where size oscillations and energy grow exponentially. For strong
interactions (Tonks-Girardeau gas), we show the effect of resonant driving on
the bosonic momentum distribution. The treatment is `exact' for zero and
infinite interactions, where the dynamics is captured by a single-variable
ordinary differential equation. For finite interactions the system is no longer
exactly solvable. For weak interactions, we show how interactions modify the
resonant behavior for weak and strong driving, using a variational
approximation which adds interactions to the single-variable description in a
controlled way.Comment: 9 pages, 8 figure
On non-canonical degrees of freedom
Non-canonical degrees of freedom provide one of the most promising routes
towards characterising a range of important phenomena in condensed matter
physics. Potential candidates include the pseudogap regime of the cuprates,
heavy-fermion behaviour, and also indeed magnetically ordered systems.
Nevertheless it remains an open question whether non-canonical algebras can in
fact provide legitimate quantum degrees of freedom. In this manuscript we
survey progress made on this topic, complementing distinct approaches so as to
obtain a unified description. In particular we obtain a novel closed-form
expression for a self-energy-like object for non-canonical degrees of freedom.
We further make a resummation of density correlations to obtain analogues of
the RPA and GW approximations commonly employed for canonical degrees of
freedom. We discuss difficulties related to generating higher-order
approximations which are consistent with conservation laws, which represents an
outstanding issue. We also discuss how the interplay between canonical and
non-canonical degrees of freedom offers a useful paradigm for organising the
phase diagram of correlated electronic behaviour.Comment: Published versio
Phases and phase transitions of a perturbed Kekul\'e-Kitaev model
We study the quantum spin liquid phase in a variant of the Kitaev model where
the bonds of the honeycomb lattice are distributed in a Kekul\'e pattern. The
system supports gapped and gapless Z_2 quantum spin liquids with interesting
differences from the original Kitaev model, the most notable being a gapped Z_2
spin liquid on a Kagome lattice. Perturbing the exactly solvable model with
antiferromagnetic Heisenberg perturbations, we find a magnetically ordered
phase stabilized by a quantum `order by disorder' mechanism, as well as an
exotic continuous phase transition between the topological spin liquid and this
magnetically ordered phase. Using a combination of field theory and Monte-Carlo
simulations, we find that the transition likely belongs to the 3D-XYxZ_2
universality class.Comment: 15 pages, 11 figure
From Interacting Particles to Equilibrium Statistical Ensembles
We argue that a particle language provides a conceptually simple framework
for the description of anomalous equilibration in isolated quantum systems. We
address this paradigm in the context of integrable models, which are those with
particles that are stable against decay. In particular, we demonstrate that a
complete description of equilibrium ensembles for interacting integrable models
requires a formulation built from the mode occupation numbers of the underlying
particle content, mirroring the case of non-interacting particles. This yields
an intuitive physical interpretation of generalized Gibbs ensembles, and
reconciles them with the microcanonical ensemble. We explain how previous
attempts to identify an appropriate ensemble overlooked an essential piece of
information, and provide explicit examples in the context of quantum quenches.Comment: 4 pages + appendice
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