SciPost Phys. 7, 021 (2019) ·
published 12 August 2019

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The dualism between superconductivity and charge/spin modulations (the
socalled stripes) dominates the phase diagram of many stronglycorrelated
systems. A prominent example is given by the Hubbard model, where these phases
compete and possibly coexist in a wide regime of electron dopings for both weak
and strong couplings. Here, we investigate this antagonism within a variational
approach that is based upon JastrowSlater wave functions, including backflow
correlations, which can be treated within a quantum Monte Carlo procedure. We
focus on clusters having a ladder geometry with $M$ legs (with $M$ ranging from
$2$ to $10$) and a relatively large number of rungs, thus allowing us a
detailed analysis in terms of the stripe length. We find that stripe order with
periodicity $\lambda=8$ in the charge and $2\lambda=16$ in the spin can be
stabilized at doping $\delta=1/8$. Here, there are no sizable superconducting
correlations and the ground state has an insulating character. A similar
situation, with $\lambda=6$, appears at $\delta=1/6$. Instead, for smaller
values of dopings, stripes can be still stabilized, but they are weakly
metallic at $\delta=1/12$ and metallic with strong superconducting correlations
at $\delta=1/10$, as well as for intermediate (incommensurate) dopings.
Remarkably, we observe that spin modulation plays a major role in stripe
formation, since it is crucial to obtain a stable striped state upon
optimization. The relevance of our calculations for previous densitymatrix
renormalization group results and for the twodimensional case is also
discussed.
Patryk Kubiczek, Alexey N. Rubtsov, Alexander I. Lichtenstein
SciPost Phys. 7, 016 (2019) ·
published 2 August 2019

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In this work we introduce a modified realtime continuoustime hybridizationexpansion quantum Monte Carlo solver for a timedependent
singleorbital Anderson impurity model: CT1/2HYBQMC. In the proposed method the diagrammatic expansion is performed only for one out of the two spin channels, while the resulting effective singleparticle problem for the other spin is solved semianalytically for each expansion diagram. CT1/2HYBQMC alleviates the dynamical sign problem by reducing the order of sampled diagrams and makes it possible to reach twice as long time scales in comparison to the standard CTHYB method. We illustrate the new solver by calculating an electric current through impurity in paramagnetic and spinpolarized cases.
Shenghan Jiang, Panjin Kim, Jung Hoon Han, Ying Ran
SciPost Phys. 7, 006 (2019) ·
published 9 July 2019

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The properties of ground state of spin$\frac{1}{2}$ kagome antiferromagnetic
Heisenberg (KAFH) model have attracted considerable interest in the past few
decades, and recent numerical simulations reported a spin liquid phase. The
nature of the spin liquid phase remains unclear. For instance, the interplay
between symmetries and $Z_2$ topological order leads to different types of
$Z_2$ spin liquid phases. In this paper, we develop a numerical simulation
method based on symmetric projected entangledpair states (PEPS), which is
generally applicable to strongly correlated model systems in two spatial
dimensions. We then apply this method to study the nature of the ground state
of the KAFH model. Our results are consistent with that the ground state is a
$U(1)$ Dirac spin liquid rather than a $Z_2$ spin liquid.
SciPost Phys. 7, 004 (2019) ·
published 5 July 2019

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We investigate the efficiency of the recently proposed Restricted Boltzmann
Machine (RBM) representation of quantum manybody states to study both the
static properties and quantum spin dynamics in the twodimensional Heisenberg
model on a square lattice. For static properties we find close agreement with
numerically exact Quantum Monte Carlo results in the thermodynamical limit. For
dynamics and small systems, we find excellent agreement with exact
diagonalization, while for systems up to N=256 spins close consistency with
interacting spinwave theory is obtained. In all cases the accuracy converges
fast with the number of network parameters, giving access to much bigger
systems than feasible before. This suggests great potential to investigate the
quantum manybody dynamics of large scale spin systems relevant for the
description of magnetic materials strongly out of equilibrium.
Malte SchÃ¼ler, Erik G. C. P. van Loon, Mikhail I. Katsnelson, Tim O. Wehling
SciPost Phys. 6, 067 (2019) ·
published 14 June 2019

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In contrast to the Hubbard model, the extended Hubbard model, which
additionally accounts for nonlocal interactions, lacks systemic studies of
thermodynamic properties especially across the metalinsulator transition.
Using a variational principle, we perform such a systematic study and describe
how nonlocal interactions screen local correlations differently in the
Fermiliquid and in the insulator. The thermodynamics reveal that nonlocal
interactions are at least in parts responsible for firstorder metalinsulator
transitions in real materials.