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Fractonic Luttinger Liquids and Supersolids in a Constrained Bose-Hubbard Model (2210.11072v2)

Published 20 Oct 2022 in cond-mat.quant-gas, cond-mat.stat-mech, cond-mat.str-el, and quant-ph

Abstract: Quantum many-body systems with fracton constraints are widely conjectured to exhibit unconventional low-energy phases of matter. In this work, we demonstrate the existence of a variety of such exotic quantum phases in the ground states of a dipole-moment conserving Bose-Hubbard model in one dimension. For integer boson fillings, we perform a mapping of the system to a model of microscopic local dipoles, which are composites of fractons. We apply a combination of low-energy field theory and large-scale tensor network simulations to demonstrate the emergence of a dipole Luttinger liquid phase. At non-integer fillings our numerical approach shows an intriguing compressible state described by a quantum Lifshitz model in which charge density-wave order coexists with dipole long-range order and superfluidity - a `dipole supersolid'. While this supersolid state may eventually be unstable against lattice effects in the thermodynamic limit, its numerical robustness is remarkable. We discuss potential experimental implications of our results.

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References (52)
  1. R. M. Nandkishore and M. Hermele, Fractons, Annu. Rev. Condens. Matter Phys. 10, 295 (2019).
  2. M. Pretko, X. Chen, and Y. You, Fracton phases of matter, Int. J. Mod. Phys. A 35, 2030003 (2020).
  3. C. Chamon, Quantum Glassiness in Strongly Correlated Clean Systems: An Example of Topological Overprotection, Phys. Rev. Lett. 94, 040402 (2005).
  4. J. Haah, Local stabilizer codes in three dimensions without string logical operators, Phys. Rev. A 83, 042330 (2011).
  5. B. Yoshida, Exotic topological order in fractal spin liquids, Physical Review B 88, 125122 (2013).
  6. S. Vijay, J. Haah, and L. Fu, A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations, Phys. Rev. B 92, 235136 (2015).
  7. M. Pretko, Subdimensional particle structure of higher rank U⁢(1)𝑈1U(1)italic_U ( 1 ) spin liquids, Phys. Rev. B 95, 115139 (2017a).
  8. M. Pretko, The fracton gauge principle, Phys. Rev. B 98, 115134 (2018).
  9. M. Pretko, Higher-spin Witten effect and two-dimensional fracton phases, Phys. Rev. B 96, 125151 (2017b).
  10. D. J. Williamson, Z. Bi, and M. Cheng, Fractonic matter in symmetry-enriched U⁢(1)𝑈1{{U}}(1)italic_U ( 1 ) gauge theory, Phys. Rev. B 100, 125150 (2019).
  11. V. Khemani, M. Hermele, and R. Nandkishore, Localization from Hilbert space shattering: From theory to physical realizations, Phys. Rev. B 101, 174204 (2020).
  12. S. Moudgalya and O. I. Motrunich, Hilbert Space Fragmentation and Commutant Algebras, Phys. Rev. X 12, 011050 (2022).
  13. A. Gromov, A. Lucas, and R. M. Nandkishore, Fracton hydrodynamics, Phys. Rev. Res. 2, 033124 (2020).
  14. A. Morningstar, V. Khemani, and D. A. Huse, Kinetically constrained freezing transition in a dipole-conserving system, Phys. Rev. B 101, 214205 (2020).
  15. P. Zhang, Subdiffusion in strongly tilted lattice systems, Phys. Rev. Res. 2, 033129 (2020).
  16. J. Iaconis, A. Lucas, and R. Nandkishore, Multipole conservation laws and subdiffusion in any dimension, Phys. Rev. E 103, 022142 (2021).
  17. A. Osborne and A. Lucas, Infinite families of fracton fluids with momentum conservation, Phys. Rev. B 105, 024311 (2022).
  18. J. Iaconis, S. Vijay, and R. Nandkishore, Anomalous subdiffusion from subsystem symmetries, Phys. Rev. B 100, 214301 (2019).
  19. J. Feldmeier, F. Pollmann, and M. Knap, Emergent fracton dynamics in a nonplanar dimer model, Phys. Rev. B 103, 094303 (2021).
  20. A. Prem, J. Haah, and R. Nandkishore, Glassy quantum dynamics in translation invariant fracton models, Phys. Rev. B 95, 155133 (2017).
  21. J. Feldmeier and M. Knap, Critically slow operator dynamics in constrained many-body systems, Phys. Rev. Lett. 127, 235301 (2021).
  22. D. Hahn, P. A. McClarty, and D. J. Luitz, Information Dynamics in a Model with Hilbert Space Fragmentation, SciPost Phys. 11, 74 (2021).
  23. M. Pretko and L. Radzihovsky, Fracton-Elasticity Duality, Phys. Rev. Lett. 120, 195301 (2018a).
  24. A. Gromov, Chiral Topological Elasticity and Fracton Order, Phys. Rev. Lett. 122, 076403 (2019).
  25. A. Kumar and A. C. Potter, Symmetry-enforced fractonicity and two-dimensional quantum crystal melting, Phys. Rev. B 100, 045119 (2019).
  26. Z. Zhai and L. Radzihovsky, Two-dimensional melting via sine-gordon duality, Phys. Rev. B 100, 094105 (2019).
  27. L. Radzihovsky, Quantum Smectic Gauge Theory, Phys. Rev. Lett. 125, 267601 (2020).
  28. Z. Zhai and L. Radzihovsky, Fractonic gauge theory of smectics, Ann. Phys. 435, 168509 (2021).
  29. M. Pretko and L. Radzihovsky, Symmetry-enriched fracton phases from supersolid duality, Phys. Rev. Lett. 121, 235301 (2018b).
  30. M. Pretko, Z. Zhai, and L. Radzihovsky, Crystal-to-fracton tensor gauge theory dualities, Phys. Rev. B 100, 134113 (2019).
  31. J.-K. Yuan, S. A. Chen, and P. Ye, Fractonic superfluids, Phys. Rev. Res. 2, 023267 (2020).
  32. S. A. Chen, J.-K. Yuan, and P. Ye, Fractonic superfluids. ii. condensing subdimensional particles, Phys. Rev. Res. 3, 013226 (2021).
  33. L. Radzihovsky, Lifshitz gauge duality, Phys. Rev. B 106, 224510 (2022).
  34. E. Lake, M. Hermele, and T. Senthil, Dipolar Bose-Hubbard model, Phys. Rev. B 106, 064511 (2022).
  35. T. Giamarchi, Quantum physics in one dimension, Vol. 121 (Clarendon press, 2003).
  36. U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. 326, 96 (2011).
  37. S. Sachdev, K. Sengupta, and S. M. Girvin, Mott Insulators in Strong Electric Fields, Phys. Rev. B 66, 075128 (2002).
  38. C. Stahl, E. Lake, and R. Nandkishore, Spontaneous breaking of multipole symmetries, Phys. Rev. B 105, 155107 (2022).
  39. A. Kapustin and L. Spodyneiko, Hohenberg-mermin-wagner-type theorems and dipole symmetry, Phys. Rev. B 106, 245125 (2022).
  40. S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
  41. M. P. Zaletel, R. S. K. Mong, and F. Pollmann, Topological characterization of fractional quantum hall ground states from microscopic hamiltonians, Phys. Rev. Lett. 110, 236801 (2013).
  42. G. Vidal, Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension, Phys. Rev. Lett. 98, 070201 (2007).
  43. S. Ejima, H. Fehske, and F. Gebhard, Dynamic properties of the one-dimensional bose-hubbard model, Europhys. Lett. 93, 30002 (2011).
  44. The dipole velocity udsubscript𝑢𝑑u_{d}italic_u start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT is determined from a delicate finite-size flow of the dipole energy gap, while kdsubscript𝑘𝑑k_{d}italic_k start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT can be robustly determined from the decay of correlation functions.
  45. F. D. M. Haldane and E. H. Rezayi, Finite-Size Studies of the Incompressible State of the Fractionally Quantized Hall Effect and its Excitations, Phys. Rev. Lett. 54, 237 (1985).
  46. S. A. Trugman and S. Kivelson, Exact results for the fractional quantum Hall effect with general interactions, Phys. Rev. B 31, 5280 (1985).
  47. E. J. Bergholtz and A. Karlhede, Half-Filled Lowest Landau Level on a Thin Torus, Phys. Rev. Lett. 94, 026802 (2005).
  48. S. Moudgalya, B. A. Bernevig, and N. Regnault, Quantum many-body scars in a Landau level on a thin torus, Phys. Rev. B 102, 195150 (2020).
  49. All data and simulation codes are available upon reasonable request at 10.5281/zenodo.7214729.
  50. J. Hauschild and F. Pollmann, Efficient numerical simulations with tensor networks: Tensor Network Python (TeNPy), SciPost Physics Lecture Notes , 5 (2018).
  51. S. Singh, R. N. C. Pfeifer, and G. Vidal, Tensor network decompositions in the presence of a global symmetry, Phys. Rev. A 82, 050301(R) (2010).
  52. S. Singh, R. N. C. Pfeifer, and G. Vidal, Tensor network states and algorithms in the presence of a global U(1) symmetry, Phys. Rev. B 83, 115125 (2011).
Citations (25)
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