29 research outputs found
Tunable quantum criticality in multi-component Rydberg arrays
Arrays of Rydberg atoms have appeared as a remarkably rich playground to
study quantum phase transitions in one dimension. One of the biggest puzzles
that was brought forward in this context is a commensurate-incommensurate phase
transitions out of density waves. Experiments report the transitions with
dynamical critical exponent that recent theoretical and numerical
analysis attribute to the appearance of chiral transitions introduced by Huse
and Fisher. However, further experimental exploration of these exotic
transitions is complicated by the narrow parameter window where chiral
transition can be realized. We argue that multi-component Rydberg arrays offer
extra experimentally controllable parameters and provide a mechanism to tune
quantum critical properties of the conformal Ashkin-Teller point that in turns
controls the extent of the chiral transition. Here we consider an effective
blockade model of two component Rydberg atoms - weak and strong components
obeying nearest- and next-nearest-neighbor blockades. When laser detuning is
applied to either strong or weak components the system is in the period-3 or
period-2 phases correspondingly. However, laser detuning used for both
components simultaneously stabilizes the period-4 phase partly surrounded by
the chiral transition. We show that the extent of the chiral transition and
even its appearance can be controlled by the relative ratio of the Rabi
frequencies of the two components.Comment: 9 pages, 10 figure
Critical properties of the Majorana chain with competing interactions
We study critical properties of a Majorana chain in the presence of two
competing interactions of the shortest possible range. The obtained phase
diagram is very rich and contains nine different phases, including three
floating, two Ising, and four gapped phases. In addition we report a wide
variety of quantum phase transitions: the supersymmetric tri-critical Ising
lines; the Lifshitz critical line characterized by the dynamical critical
exponent ; Kosterlitz-Thouless transitions, and an exotic first order
transition between the floating and the gapped phases. However, the most
surprising feature of the obtained phase diagram is the emergence of the
commensurate line at which the floating phases collapses into direct
transition. We provide numerical evidences that the resulting multi-critical
point belongs to the universality class of the eight-vertex model. Implications
in the context of supersymmetric properties of the Majorana chain is briefly
discussed.Comment: 12 pages, 13 figure
Floating, critical and dimerized phases in a frustrated spin-3/2 chain
We study spontaneous dimerization and emergent criticality in a spin-3/2
chain with antiferromagnetic nearest-neighbor , next-nearest-neighbor
and three-site interactions. In the absence of three-site
interaction , we provide evidence that the model undergoes a remarkable
sequence of three phase transitions as a function of , going
successively through a critical commesurate phase, a partially dimerized gapped
phase, a critical floating phase with quasi-long-range incommensurate order, to
end up in a fully dimerized phase at very large . In the field theory
language, this implies that the coupling constant of the marginal operator
responsible for dimerization changes sign three times. For large enough ,
the fully dimerized phase is stabilized for all , and the phase
transitions between the critical phases and this phase are both
Wess-Zumino-Witten (WZW) SU(2) along part of the boundary and turn first
order at some point due to the presence of a marginal operator in the WZW
SU(2) model. By contrast, the transition between the two dimerized phase is
always first order, and the phase transitions between the partially dimerized
phase and the critical phases are Kosterlitz-Thouless. Finally, we discuss the
intriguing spin-1/2 edge states that emerge in the partially dimerized phase
for even chains. Unlike their counterparts in the spin-1 chain, they are not
confined and disappear upon increasing in favour of a reorganization of
the dimerization pattern.Comment: 14 pages, 23 figure
DMRG investigation of constrained models: from quantum dimer and quantum loop ladders to hard-boson and Fibonacci anyon chains
Motivated by the presence of Ising transitions that take place entirely in
the singlet sector of frustrated spin-1/2 ladders and spin-1 chains, we study
two types of effective dimer models on ladders, a quantum dimer model and a
quantum loop model. Building on the constraints imposed on the dimers, we
develop a Density Matrix Renormalization Group algorithm that takes full
advantage of the relatively small Hilbert space that only grows as Fibonacci
number. We further show that both models can be mapped rigorously onto a
hard-boson model first studied by Fendley, Sengupta and Sachdev [Phys. Rev. B
69, 075106 (2004)], and combining early results with recent results obtained
with the present algorithm on this hard-boson model, we discuss the full phase
diagram of these quantum dimer and quantum loop models, with special emphasis
on the phase transitions. In particular, using conformal field theory, we fully
characterize the Ising transition and the tricritical Ising end point, with a
complete analysis of the boundary-field correspondence for the tricritical
Ising point including partially polarized edges. Finally, we show that the
Fibonacci anyon chain is exactly equivalent to special critical points of these
models.Comment: 29 pages, 20 figures; Submission to SciPos
Kibble-Zurek exponent and chiral transition of the period-4 phase of Rydberg chains
Chains of Rydberg atoms have emerged as an amazing playground to study
quantum physics in 1D. Playing with inter-atomic distances and laser detuning,
one can in particular explore the commensurate-incommensurate transition out of
charge-density waves through the Kibble-Zurek mechanism, and the possible
presence of a chiral transition with dynamical exponent . Here we address
this problem theoretically with effective blockade models where the
short-distance repulsions are replaced by a constraint of no double occupancy.
For the period-4 phase, we show there is an Ashkin-Teller transition point with
exponent surrounded by a direct chiral transition with a dynamical
exponent and a Kibble-Zurek exponent . For Rydberg atoms with
a van der Waals potential, we suggest that the experimental value is
due to a chiral transition with and surrounding
an Ashkin-Teller transition close to the 4-state Potts universality.Comment: 10 pages, 10 figures + supplemental materia