Efficiently calculating the Luttinger liquid parameter with crosscap states in incommensurate phases
ORAL
Abstract
The Tomonaga–Luttinger liquid (TLL) model captures the low-energy properties of many gapless 1D systems, where ground state correlations are governed by the Luttinger parameter K. When K reaches a critical value, the TLL becomes unstable, driving an infinite-order Berezinskii–Kosterlitz–Thouless (BKT) quantum phase transition. In a spin-center-based analog quantum simulator of the interacting Kitaev chain, we find that entanglement entropy does not efficiently identify BKT transitions between floating and Z2 symmetry-breaking phases. Instead, we efficiently locate these transitions by calculating K using novel conformal field theory (CFT) methods, particularly with tensor networks via the overlap of the ground state and a crosscap state. In floating phases, where ground states are incommensurate and mix particle-number sectors, this overlap generally fails to yield accurate K. We calculate Hamiltonian parameters where the ground state is nearly confined to a single particle-number sector, allowing a projected crosscap overlap approach to reliably determine K even within the floating phases.
*Computations were performed using the computer clusters and data storage resources of the HPCC, which were funded by grants from NSF (MRI-2215705, MRI-1429826) and NIH (1S10OD016290-01A1). J.Z. is supported by NSFC under Grants No. 12304172 and No. 12347101, CNSF under Grant No. CSTB2023NSCQ-MSX0048 and No. CSTB2024YCJH-KYXM0064.
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Publication:Losey, T., Zhang, J., & Tsai, S.-W. (2025). Calculating the Luttinger liquid parameter for an interacting Kitaev chain quantum simulator. arXiv preprint arXiv:2510.19189. Tan, B. Y., Zhang, Y., Zhang, H. C., Tang, W., Wang, L., Tu, H. H., & Wu, Y. H. (2025). Extracting the Luttinger parameter from a single wave function. Physical Review Letters, 134(7), 076501. Losey, T., Candido, D. R., Zhang, J., Meurice, Y., Flatté, M. E., & Tsai, S.-W. (2024). Quantum simulation of the spin-1/2 XYZ model using solid-state spin centers. Editor's Suggestions, Physical Review B, 110(1), 014413.
