Lukas Weber, Andreas Honecker, Bruce Normand, Philippe Corboz, Frédéric Mila, Stefan Wessel
SciPost Phys. 12, 054 (2022) ·
published 8 February 2022
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The phase diagrams of highly frustrated quantum spin systems can exhibit
first-order quantum phase transitions and thermal critical points even in the
absence of any long-ranged magnetic order. However, all unbiased numerical
techniques for investigating frustrated quantum magnets face significant
challenges, and for generic quantum Monte Carlo methods the challenge is the
sign problem. Here we report on a general quantum Monte Carlo approach with a
loop-update scheme that operates in any basis, and we show that, with an
appropriate choice of basis, it allows us to study a frustrated model of
coupled spin-1/2 trimers: simulations of the trilayer Heisenberg
antiferromagnet in the spin-trimer basis are sign-problem-free when the
intertrimer couplings are fully frustrated. This model features a first-order
quantum phase transition, from which a line of first-order transitions emerges
at finite temperatures and terminates in a thermal critical point. The trimer
unit cell hosts an internal degree of freedom that can be controlled to induce
an extensive entropy jump at the quantum transition, which alters the shape of
the first-order line. We explore the consequences for the thermal properties in
the vicinity of the critical point, which include profound changes in the lines
of maxima defined by the specific heat. Our findings reveal trimer quantum
magnets as fundamental systems capturing in full the complex thermal physics of
the strongly frustrated regime.
SciPost Phys. 12, 006 (2022) ·
published 6 January 2022
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The excitation ansatz for tensor networks is a powerful tool for simulating
the low-lying quasiparticle excitations above ground states of strongly
correlated quantum many-body systems. Recently, the two-dimensional tensor
network class of infinite entangled pair states gained new ground state
optimization methods based on automatic differentiation, which are at the same
time highly accurate and simple to implement. Naturally, the question arises
whether these new ideas can also be used to optimize the excitation ansatz,
which has recently been implemented in two dimensions as well. In this paper,
we describe a straightforward way to reimplement the framework for excitations
using automatic differentiation, and demonstrate its performance for the
Hubbard model at half filling.
Korbinian Kottmann, Philippe Corboz, Maciej Lewenstein, Antonio Acín
SciPost Phys. 11, 025 (2021) ·
published 9 August 2021
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We demonstrate how to map out the phase diagram of a two dimensional quantum
many body system with no prior physical knowledge by applying deep
\textit{anomaly detection} to ground states from infinite projected entangled
pair state simulations. As a benchmark, the phase diagram of the 2D frustrated
bilayer Heisenberg model is analyzed, which exhibits a second-order and two
first-order quantum phase transitions. We show that in order to get a good
qualitative picture of the transition lines, it suffices to use data from the
cost-efficient simple update optimization. Results are further improved by
post-selecting ground-states based on their energy at the cost of contracting
the tensor network once. Moreover, we show that the mantra of ``more training
data leads to better results'' is not true for the learning task at hand and
that, in principle, one training example suffices for this learning task. This
puts the necessity of neural network optimizations for these learning tasks in
question and we show that, at least for the model and data at hand, a simple
geometric analysis suffices.
SciPost Phys. 3, 030 (2017) ·
published 28 October 2017
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Using infinite projected entangled pair states, we study the ground state
phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square
lattice directly in the thermodynamic limit. We find an unexpected partially
nematic partially magnetic phase in between the antiferroquadrupolar and
ferromagnetic regions. Furthermore, we describe all observed phases and discuss
the nature of the phase transitions involved.