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 $z>1$ 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 $z=3$; 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 $J_1$, next-nearest-neighbor $J_2$ and three-site $J_3$ interactions. In the absence of three-site interaction $J_3$, we provide evidence that the model undergoes a remarkable sequence of three phase transitions as a function of $J_2/J_1$, 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 $J_2/J_1$. 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 $J_3$, the fully dimerized phase is stabilized for all $J_2$, and the phase transitions between the critical phases and this phase are both Wess-Zumino-Witten (WZW) SU(2)$_3$ 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)$_3$ 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 $J_2$ 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 $z>1$. 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 $\nu=0.78$ surrounded by a direct chiral transition with a dynamical exponent $z=1.14$ and a Kibble-Zurek exponent $\mu=0.4$. For Rydberg atoms with a van der Waals potential, we suggest that the experimental value $\mu=0.25$ is due to a chiral transition with $z\simeq 1.9$ and $\nu\simeq 0.47$ surrounding an Ashkin-Teller transition close to the 4-state Potts universality.Comment: 10 pages, 10 figures + supplemental materia