Jiaju Zhang, Pasquale Calabrese, Marcello Dalmonte, M. A. Rajabpour
SciPost Phys. Core 2, 007 (2020) ·
published 7 May 2020

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We carry out a comprehensive comparison between the exact modular Hamiltonian
and the lattice version of the BisognanoWichmann (BW) one in onedimensional
critical quantum spin chains. As a warmup, we first illustrate how the trace
distance provides a more informative mean of comparison between reduced density
matrices when compared to any other Schatten $n$distance, normalized or not.
In particular, as noticed in earlier works, it provides a way to bound other
correlation functions in a precise manner, i.e., providing both lower and upper
bounds. Additionally, we show that two close reduced density matrices, i.e.
with zero trace distance for large sizes, can have very different modular
Hamiltonians. This means that, in terms of describing how two states are close
to each other, it is more informative to compare their reduced density matrices
rather than the corresponding modular Hamiltonians. After setting this
framework, we consider the ground states for infinite and periodic XX spin
chain and critical Ising chain. We provide robust numerical evidence that the
trace distance between the lattice BW reduced density matrix and the exact one
goes to zero as $\ell^{2}$ for large length of the interval $\ell$. This
provides strong constraints on the difference between the corresponding
entanglement entropies and correlation functions. Our results indicate that
discretized BW reduced density matrices reproduce exact entanglement entropies
and correlation functions of local operators in the limit of large subsystem
sizes. Finally, we show that the BW reduced density matrices fall short of
reproducing the exact behavior of the logarithmic emptiness formation
probability in the ground state of the XX spin chain.
SciPost Phys. 8, 042 (2020) ·
published 16 March 2020

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Variational wave functions have been a successful tool to investigate the
properties of quantum spin liquids. Finding their parent Hamiltonians is of
primary interest for the experimental simulation of these strongly correlated
phases, and for gathering additional insights on their stability. In this work,
we systematically reconstruct approximate spinchain parent Hamiltonians for
JastrowGutzwiller wave functions, which share several features with quantum
spin liquid wavefunctions in two dimensions. Firstly, we determine the
different phases encoded in the parameter space through their correlation
functions and entanglement content. Secondly, we apply a recently proposed
entanglementguided method to reconstruct parent Hamiltonians to these states,
which constrains the search to operators describing relativistic lowenergy
field theories  as expected for deconfined phases of gauge theories relevant
to quantum spin liquids. The quality of the results is discussed using
different quantities and comparing to exactly known parent Hamiltonians at
specific points in parameter space. Our findings provide guiding principles for
experimental Hamiltonian engineering of this class of states.
Ferdinand Tschirsich, Simone Montangero, Marcello Dalmonte
SciPost Phys. 6, 028 (2019) ·
published 6 March 2019

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We investigate the ground state phase diagram of square ice  a U(1) lattice
gauge theory in two spatial dimensions  using gauge invariant tensor network
techniques. By correlation function, Wilson loop, and entanglement diagnostics,
we characterize its phases and the transitions between them, finding good
agreement with previous studies. We study the entanglement properties of string
excitations on top of the ground state, and provide direct evidence of the fact
that the latter are described by a conformal field theory. Our results pave the
way to the application of tensor network methods to confining, twodimensional
lattice gauge theories, to investigate their phase diagrams and lowlying
excitations.
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