Geometric scaling in the quantum Hall system

X. R. Wang, Gang Xiong, S. D. Wang +2 more

Jia‐Wei Mei, Evelyn Tang, Xiao-Gang Wen

We study quantum spin systems with a proper combination of geometric frustration, spin-orbit coupling and ferromagnetism. We argue that such a system is likely to be in a chiral spin state, a fractional quantum Hall (FQH) state for bosonic spin degrees of freedom. The energy scale of the bosonic FQH state is of the same order as the spin-orbit coupling and ferromagnetism --- overall much higher than the energy scale of FQH states in semiconductors.

H. P. Wei, Daniel C. Tsui, Adrianus M. M. Pruisken

Tanima Chanda, Simrandeep Kaur, Anantbir Virk +5 more

At continuous electronic phase transitions, Coulomb interactions can modify the relation between length, energy, and temperature, but experimentally disentangling their effects on spatial versus dynamical criticality has remained difficult, since finite-temperature scaling alone measures only the combined exponent $κ= 1/(zγ)$. Here, we introduce two advances that resolve this limitation. First, by combining temperature scaling with independent current scaling, we separately extract the dynamical exponent $z$ and the localization-length exponent $γ$ at the quantum Hall plateau transition -- rather than inferring one from an assumed value of the other. Second, using dual-graphite-gated graphene devices in which the effective Coulomb interaction range is tuned geometrically by the ratio of the magnetic length $l_B$ to the graphite-gate distance $d$, we track this separation across both screened and unscreened interaction regimes within the same device platform. Temperature scaling gives $κ\simeq 0.21$ in the screened regime and $κ\simeq 0.41$ in the unscreened regime; combining this with current scaling reveals that screening changes $z$ from $\simeq 1$ in the unscreened regime to $\simeq 2$ in the screened regime. In contrast, $γ$ remains close to $2.4$ throughout. Our results establish that gate-controlled screening selectively modifies the interaction-dependent dynamical sector of the quantum Hall transition, leaving the localization-length exponent $γ$ unchanged within experimental uncertainty. More broadly, this work establishes geometric screening as a versatile tool for controlling interactions and disentangling interaction and disorder effects in correlated two-dimensional systems, including fractional quantum Hall states, moiré materials, and other strongly localized electronic phases.

Hideo Aoki

Ammar A. Kirmani, Kieran Bull, Chang-Yu Hou +5 more

Intermediate-scale quantum technologies provide new opportunities for scientific discovery, yet they also pose the challenge of identifying suitable problems that can take advantage of such devices in spite of their present-day limitations. In solid-state materials, fractional quantum Hall phases continue to attract attention as hosts of emergent geometrical excitations analogous to gravitons, resulting from the nonperturbative interactions between the electrons. However, the direct observation of such excitations remains a challenge. Here, we identify a quasi-one-dimensional model that captures the geometric properties and graviton dynamics of fractional quantum Hall states. We then simulate geometric quench and the subsequent graviton dynamics on the IBM quantum computer using an optimally compiled Trotter circuit with bespoke error mitigation. Moreover, we develop an efficient, optimal-control-based variational quantum algorithm that can efficiently simulate graviton dynamics in larger systems. Our results open a new avenue for studying the emergence of gravitons in a new class of tractable models on the existing quantum hardware.