51 research outputs found
Current operators in integrable spin chains: lessons from long range deformations
We consider the finite volume mean values of current operators in integrable
spin chains with local interactions, and provide an alternative derivation of
the exact result found recently by the author and two collaborators. We use a
certain type of long range deformation of the local spin chains, which was
discovered and explored earlier in the context of the AdS/CFT correspondence.
This method is immediately applicable also to higher rank models: as a concrete
example we derive the current mean values in the SU(3)-symmetric fundamental
model, solvable by the nested Bethe Ansatz. The exact results take the same
form as in the Heisenberg spin chains: they involve the one-particle
eigenvalues of the conserved charges and the inverse of the Gaudin matrix.Comment: 21 pages, v2: minor change
Finite volume form factors and correlation functions at finite temperature
In this thesis we investigate finite size effects in 1+1 dimensional
integrable QFT. In particular we consider matrix elements of local operators
(finite volume form factors) and vacuum expectation values and correlation
functions at finite temperature. In the first part of the thesis we give a
complete description of the finite volume form factors in terms of the infinite
volume form factors (solutions of the bootstrap program) and the S-matrix of
the theory. The calculations are correct to all orders in the inverse of the
volume, only exponentially decaying (residual) finite size effects are
neglected. We also consider matrix elements with disconnected pieces and
determine the general rule for evaluating such contributions in a finite
volume. The analytic results are tested against numerical data obtained by the
truncated conformal space approach in the Lee-Yang model and the Ising model in
a magnetic field. In a separate section we also evaluate the leading
exponential correction (the -term) associated to multi-particle energies
and matrix elements. In the second part of the thesis we show that finite
volume factors can be used to derive a systematic low-temperature expansion for
correlation functions at finite temperature. In the case of vacuum expectation
values the series is worked out up to the third non-trivial order and a
complete agreement with the LeClair-Mussardo formula is observed. A preliminary
treatment of the two-point function is also given by considering the first
nontrivial contributions.Comment: PhD thesis, 141 page
Algebraic construction of current operators in integrable spin chains
Generalized Hydrodynamics is a recent theory that describes the large scale
transport properties of one dimensional integrable models. At the heart of this
theory lies an exact quantum-classical correspondence, which states that the
flows of the conserved quantities are essentially quasi-classical even in the
interacting quantum many body models. We provide the algebraic background to
this observation, by embedding the current operators of the integrable spin
chains into the canonical framework of Yang-Baxter integrability. Our
construction can be applied in a large variety of models including the XXZ spin
chains, the Hubbard model, and even in models lacking particle conservation
such as the XYZ chain. Regarding the XXZ chain we present a simplified proof of
the recent exact results for the current mean values, and explain how their
quasi-classical nature emerges from the exact computations.Comment: 4+epsilon pages, and Supp. Mat. 5 page
On factorized overlaps: Algebraic Bethe Ansatz, twists, and Separation of Variables
We investigate the exact overlaps between eigenstates of integrable spin
chains and a special class of states called "integrable initial/final states".
These states satisfy a special integrability constraint, and they are closely
related to integrable boundary conditions. We derive new algebraic relations
for the integrable states, which lead to a set of recursion relations for the
exact overlaps. We solve these recursion relations and thus we derive new
overlap formulas, valid in the XXX Heisenberg chain and its integrable higher
spin generalizations. Afterwards we generalize the integrability condition to
twisted boundary conditions, and derive the corresponding exact overlaps.
Finally, we embed the integrable states into the "Separation of Variables"
framework, and derive an alternative representation for the exact overlaps of
the XXX chain. Our derivations and proofs are rigorous, and they can form the
basis of future investigations involving more complicated models such as nested
or long-range deformed systems.Comment: 34 pages, 3 figures; v2: references added, minor modifications, v3:
minor modificatio
Current mean values in the XYZ model
The XYZ model is an integrable spin chain which has an infinite set of
conserved charges, but it lacks a global -symmetry. We consider the
current operators, which describe the flow of the conserved quantities in this
model. We derive an exact result for the current mean values, valid for any
eigenstate in a finite volume with periodic boundary conditions. This result
can serve as a basis for studying the transport properties of this model within
Generalized Hydrodynamics.Comment: 27 page
Tensor network decompositions for absolutely maximally entangled states
Absolutely maximally entangled (AME) states of qudits (also known as
perfect tensors) are quantum states that have maximal entanglement for all
possible bipartitions of the sites/parties. We consider the problem of whether
such states can be decomposed into a tensor network with a small number of
tensors, such that all physical and all auxiliary spaces have the same
dimension . We find that certain AME states with can be decomposed
into a network with only three 4-leg tensors; we provide concrete solutions for
local dimension and higher. Our result implies that certain AME states
with six parties can be created with only three two-site unitaries from a
product state of three Bell pairs, or equivalently, with six two-site unitaries
acting on a product state on six qudits. We also consider the problem for
, where we find similar tensor network decompositions with six 4-leg
tensors.Comment: 21 page
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