SciPost Phys. 14, 152 (2023) ·
published 13 June 2023
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We study Majorana chain with the shortest possible interaction term and in the presence of hopping alternation. When formulated in terms of spins the model corresponds to the transverse field Ising model with nearest-neighbor transverse and next-nearest-neighbor longitudinal repulsion. The phase diagram obtained with extensive DMRG simulations is very rich and contains six phases. Four gapped phases include paramagnetic, period-2 with broken translation symmetry, $\mathbb{Z}_2$ with broken parity symmetry and the period-2-$\mathbb{Z}_2$ phase with both symmetries broken. In addition there are two floating phases: gapless and critical Luttinger liquid with incommensurate correlations, and with an additional spontaneously broken $\mathbb{Z}_2$ symmetry in one of them. By analyzing an extended phase diagram we demonstrate that, in contrast with a common belief, the Luttinger liquid phase along the self-dual critical line terminates at a weaker interaction strength than the end point of the Ising critical line that we find to be in the tri-critical Ising universality class. We also show that none of these two points is a Lifshitz point terminating the incommensurability. In addition, we analyzed topological properties through Majorana zero modes emergent in the two topological phases, with and without incommensurability. In the weak interaction regime, a self-consistent mean-field treatment provides a remarkable accuracy for the description of the spectral pairing and the parity switches induced by the interaction.
SciPost Phys. 6, 050 (2019) ·
published 29 April 2019
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We study the many-body localization (MBL) properties of a chain of
interacting fermions subject to a quasiperiodic potential such that the
non-interacting chain is always delocalized and displays multifractality.
Contrary to naive expectations, adding interactions in this systems does not
enhance delocalization, and a MBL transition is observed. Due to the local
properties of the quasiperiodic potential, the MBL phase presents specific
features, such as additional peaks in the density distribution. We furthermore
investigate the fate of multifractality in the ergodic phase for low potential
values. Our analysis is based on exact numerical studies of eigenstates and
dynamical properties after a quench.
SciPost Phys. 2, 011 (2017) ·
published 24 March 2017
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Using quantum Monte Carlo simulations, we compute the participation
(Shannon-R\'enyi) entropies for groundstate wave functions of Heisenberg
antiferromagnets for one-dimensional (line) subsystems of length $L$ embedded
in two-dimensional ($L\times L$) square lattices. We also study the line
entropy at finite temperature, i.e. of the diagonal elements of the density
matrix, for three-dimensional ($L\times L\times L$) cubic lattices. The
breaking of SU(2) symmetry is clearly captured by a universal logarithmic
scaling term $l_q\ln L$ in the R\'enyi entropies, in good agreement with the
recent field-theory results of Misguish, Pasquier and Oshikawa
[arXiv:1607.02465]. We also study the dependence of the log prefactor $l_q$ on
the R\'enyi index $q$ for which a transition is detected at $q_c\simeq 1$.
Submissions
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Dr Laflorencie: "Report 1 by Dirk Schuricht on ..."
in Submissions | report on Topological and quantum critical properties of the interacting Majorana chain model