arXiv subjects

Shu-Ao Liao

Publications and source records attributed to Shu-Ao Liao.

2 recordsLinked to original sources

arXiv2026

Luttinger liquid parameters in one-dimensional Rydberg arrays

We investigate Berezinskii-Kosterlitz-Thouless (BKT) transitions in one-dimensional Rydberg chains, where commensurate critical regimes associated with the melting of crystalline orders with period larger than five and incommensurate floating phases are both described by Luttinger liquid theory. The central quantity is the Luttinger liquid parameter $K$, which characterizes the universal low-energy theory and controls the relevance of perturbations driving BKT transitions. We extract $K$ using Friedel oscillations and the recently developed crosscap method introduced in Phys. Rev. Lett. 134, 076501 (2025). As benchmarks, we first apply the crosscap method to a $\mathbb{Z}_3$ dual hard-core boson chain and a spin-1 XY chain with single-ion anisotropy, obtaining BKT transition points consistent with previous results after finite-size extrapolation. We then compute $K$ in the Rydberg chain along lines with fixed correlation-oscillation period near BKT transitions. Along the commensurate period-five line, the critical values of $K$ predicted by sine-Gordon theory reveal two BKT transitions separating the disordered phase, the critical phase, and the $\mathbb{Z}_5$ crystalline phase. The results from Friedel oscillations and the crosscap method agree with each other and are further supported by energy-gap scaling and Binder-cumulant analysis. To obtain reliable values of $K$ from Friedel oscillations, we use a multi-harmonic fitting scheme throughout the analysis. Along incommensurate lines, the BKT points obtained from Friedel oscillations agree with those extracted from entanglement entropy. Finally, we show that the values of $K$ obtained from the two methods are mutually consistent inside the incommensurate floating phase.

cond-mat.quant-gas↗

arXiv2024

Phase diagram of Rydberg atoms in a two-leg rectangular ladder

Using the density matrix renormalization group algorithm, we map the ground-state phase diagram of a two-leg Rydberg ladder array with lattice spacings $a_x=2a_y$. We identify various density wave phases that spontaneously break the translational symmetry or the top-bottom reflection symmetry within the ladder. By increasing the laser detuning from zero, where the system is in a disordered phase that preserves all symmetries, we observe density wave orders with spontaneous breaking of the translational $\mathbb{Z}_p$ symmetries at intermediate detuning values, while the reflection symmetry is preserved. These orders exhibit nonzero bond orders with positive expectation values on every $p$th rung, thus labeled as $\mathbb{Z}_p^+$ phases. At larger detuning values, another spontaneous breaking of the reflection symmetry, which disrupted the bond orders on the rungs, occurs via an Ising phase transition. In these phases, either the top or the bottom site is occupied in a staggered way on every $p$th rung, breaking the translational $\mathbb{Z}_{2p}$ symmetry, thus labeled by $\mathbb{Z}_{2p}$ phases. We locate and characterize the 3-state Potts point and Ashkin-Teller point along the commensurate lines, as well as the direct chiral phase transitions between the disordered phase and the $\mathbb{Z}_p^+$ ($p = 3, 4$) phases. Critical exponents $ν$ and $z$ are calculated for both conformal and chiral phase transition points. We finally identify two types of floating phases in the phase diagram: one characterized by a quasi-long-range incommensurate bond-order wave, and the other by a quasi-long-range incommensurate wave of density differences in the rungs. Our work motivates further applications of Rydberg atom arrays in quantum simulation.

cond-mat.quant-gas↗