Power-law scalings in weakly-interacting Bose gases at quantum criticality

doi:10.1007/s11467-022-1186-x

Frontiers of Physics

2022, Vol. 17

Issue (6): 61501 https://doi.org/10.1007/s11467-022-1186-x

本期目录

Power-law scalings in weakly-interacting Bose gases at quantum criticality

Ming-Cheng Liang^1,², Zhi-Xing Lin¹, Yang-Yang Chen^3,⁴, Xi-Wen Guan^3,⁵, Xibo Zhang^1,^2,⁶(

)

¹. International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
². Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
³. State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
⁴. Institute of Modern Physics, Northwest University, Xi'an 710127, China
⁵. Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia
⁶. Beijing Academy of Quantum Information Sciences, Beijing 100193, China

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Abstract：

Weakly interacting quantum systems in low dimensions have been investigated for a long time, but there still remain a number of open questions and a lack of explicit expressions of physical properties of such systems. In this work, we find power-law scalings of thermodynamic observables in low-dimensional interacting Bose gases at quantum criticality. We present a physical picture for these systems with the repulsive interaction strength approaching zero; namely, the competition between the kinetic and interaction energy scales gives rise to power-law scalings with respect to the interaction strength in characteristic thermodynamic observables. This prediction is supported by exact Bethe ansatz solutions in one dimension, demonstrating a simple 1/3-power-law scaling of the critical entropy per particle. Our method also yields results in agreement with a non-perturbative renormalization-group computation in two dimensions. These results provide a new perspective for understanding many-body phenomena induced by weak interactions in quantum gases.

Key words： power-law scaling quantum criticality Bose gases weak interaction non-perturbative methods

收稿日期: 2022-05-17 出版日期: 2022-07-15

Corresponding Author(s): Xibo Zhang

引用本文:

. [J]. Frontiers of Physics, 2022, 17(6): 61501.
Ming-Cheng Liang, Zhi-Xing Lin, Yang-Yang Chen, Xi-Wen Guan, Xibo Zhang. Power-law scalings in weakly-interacting Bose gases at quantum criticality. Front. Phys. , 2022, 17(6): 61501.

链接本文:

https://academic.hep.com.cn/fop/CN/10.1007/s11467-022-1186-x
https://academic.hep.com.cn/fop/CN/Y2022/V17/I6/61501

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1	D. Lee T. , Huang K. , N. Yang C. . Eigenvalues and eigenfunctions of a Bose system of hard spheres and its low-temperature properties. Phys. Rev., 1957, 106( 6): 1135 https://doi.org/10.1103/PhysRev.106.1135
2	N. Yang C. , P. Yang C. . Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. J. Math. Phys., 1969, 10( 7): 1115 https://doi.org/10.1063/1.1664947
3	Dalfovo F. , Giorgini S. , P. Pitaevskii L. , Stringari S. . Theory of Bose−Einstein condensation in trapped gases. Rev. Mod. Phys., 1999, 71( 3): 463 https://doi.org/10.1103/RevModPhys.71.463
4	Prokof’ev N. , Ruebenacker O. , Svistunov B. . Critical point of a weakly interacting two-dimensional Bose gas. Phys. Rev. Lett., 2001, 87( 27): 270402 https://doi.org/10.1103/PhysRevLett.87.270402
5	Prokof’ev N. , Svistunov B. . Two-dimensional weakly interacting Bose gas in the fluctuation region. Phys. Rev. A, 2002, 66( 4): 043608 https://doi.org/10.1103/PhysRevA.66.043608
6	Floerchinger S. , Wetterich C. . Nonperturbative thermodynamics of an interacting Bose gas. Phys. Rev. A, 2009, 79( 6): 063602 https://doi.org/10.1103/PhysRevA.79.063602
7	Z. Jiang Y. , Y. Chen Y. , W. Guan X. . Understanding many-body physics in one dimension from the Lieb–Liniger model. Chin. Phys. B, 2015, 24( 5): 050311 https://doi.org/10.1088/1674-1056/24/5/050311
8	Chin C. . Ultracold atomic gases going strong. Natl. Sci. Rev., 2016, 3( 2): 168 https://doi.org/10.1093/nsr/nwv073
9	Bettelheim E. . The Whitham approach to the c → 0 limit of the Lieb–Liniger model and generalized hydrodynamics. J. Phys. A Math. Theor., 2020, 53( 20): 205204 https://doi.org/10.1088/1751-8121/ab8676
10	Posazhennikova A. . Colloquium: Weakly interacting, dilute Bose gases in 2D. Rev. Mod. Phys., 2006, 78( 4): 1111 https://doi.org/10.1103/RevModPhys.78.1111
11	W. Guan X. , T. Batchelor M. , Lee C. . Fermi gases in one dimension: From Bethe ansatz to experiments. Rev. Mod. Phys., 2013, 85( 4): 1633 https://doi.org/10.1103/RevModPhys.85.1633
12	Gaudin M. . Un systeme a une dimension de fermions en interaction. Phys. Lett. A, 1967, 24( 1): 55 https://doi.org/10.1016/0375-9601(67)90193-4
13	N. Yang C. . Some exact results for the many-body problem in one dimension with repulsive δ-function interaction. Phys. Rev. Lett., 1967, 19( 23): 1312 https://doi.org/10.1103/PhysRevLett.19.1312
14	Takahashi M. . Ground state energy of the one-dimensional electron system with short-range interaction (I). Prog. Theor. Phys., 1970, 44 : 348 https://doi.org/10.1143/PTP.44.348
15	Iida T. , Wadati M. . Exact analysis of a one-dimensional attractive δ-function Fermi gas with arbitrary spin polarization. J. Low Temp. Phys., 2007, 148( 3−4): 417 https://doi.org/10.1007/s10909-007-9409-7
16	W. Guan X. . Polaron, molecule and pairing in one-dimensional spin-1/2 Fermi gas with an attractive delta-function interaction. Front. Phys., 2012, 7( 1): 8 https://doi.org/10.1007/s11467-011-0213-0
17	W. Guan X. , Q. Ma Z. . One-dimensional multicomponent fermions with δ-function interaction in strong- and weak-coupling limits: Two-component Fermi gas. Phys. Rev. A, 2012, 85( 3): 033632 https://doi.org/10.1103/PhysRevA.85.033632
18	W. Guan X. , Q. Ma Z. , Wilson B. . One-dimensional multicomponent fermions with δ -function interaction in strong- and weak-coupling limits: κ-component Fermi gas. Phys. Rev. A, 2012, 85( 3): 033633 https://doi.org/10.1103/PhysRevA.85.033633
19	A. Tracy C. , Widom H. . On the ground state energy of the δ-function Bose gas. J. Phys. A Math. Theor., 2016, 49( 29): 294001 https://doi.org/10.1088/1751-8113/49/29/294001
20	A. Tracy C. , Widom H. . On the ground state energy of the δ-function Fermi gas. J. Math. Phys., 2016, 57( 10): 103301 https://doi.org/10.1063/1.4964252
21	Prolhac S. . Ground state energy of the δ-Bose and Fermi gas at weak coupling from double extrapolation. J. Phys. A Math. Theor., 2017, 50( 14): 144001 https://doi.org/10.1088/1751-8121/aa5e00
22	Sachdev S., Quantum Phase Transitions, 2nd Ed., Cambridge University Press, 2011
23	G. Batrouni G. , T. Scalettar R. , T. Zimanyi G. . Quantum critical phenomena in one-dimensional Bose systems. Phys. Rev. Lett., 1990, 65( 14): 1765 https://doi.org/10.1103/PhysRevLett.65.1765
24	Bloch I. , Dalibard J. , Zwerger W. . Many-body physics with ultracold gases. Rev. Mod. Phys., 2008, 80( 3): 885 https://doi.org/10.1103/RevModPhys.80.885
25	A. Cazalilla M. , Citro R. , Giamarchi T. , Orignac E. , Rigol M. . One dimensional bosons: From condensed matter systems to ultracold gases. Rev. Mod. Phys., 2011, 83( 4): 1405 https://doi.org/10.1103/RevModPhys.83.1405
26	Chin C. Universal Themes of Bose−Einstein Condensation in: by D. Snoke edited Proukakis N. Littlewood P., Cambridge University Press, 2017, Chapter 9, pp 175– 195
27	L. Ho T. . Universal thermodynamics of degenerate quantum gases in the unitarity limit. Phys. Rev. Lett., 2004, 92( 9): 090402 https://doi.org/10.1103/PhysRevLett.92.090402
28	L. Ho T. , Zhou Q. . Obtaining the phase diagram and thermodynamic quantities of bulk systems from the densities of trapped gases. Nat. Phys., 2010, 6( 2): 131 https://doi.org/10.1038/nphys1477
29	Pilati S. , Giorgini S. , Prokof’ev N. . Critical temperature of interacting Bose gases in two and three dimensions. Phys. Rev. Lett., 2008, 100( 14): 140405 https://doi.org/10.1103/PhysRevLett.100.140405
30	Rançon A. , Dupuis N. . Universal thermodynamics of a two-dimensional Bose gas. Phys. Rev. A, 2012, 85( 6): 063607 https://doi.org/10.1103/PhysRevA.85.063607
31	Kinast J. , Turlapov A. , E. Thomas J. , Chen Q. , Stajic J. , Levin K. . Heat capacity of a strongly interacting Fermi gas. Science, 2005, 307( 5713): 1296 https://doi.org/10.1126/science.1109220
32	Luo L. , E. Thomas J. . Thermodynamic measurements in a strongly interacting Fermi gas. J. Low Temp. Phys., 2009, 154( 1−2): 1 https://doi.org/10.1007/s10909-008-9850-2
33	Nascimbène S. , Navon N. , J. Jiang K. , Chevy F. , Salomon C. . Exploring the thermodynamics of a universal Fermi gas. Nature, 2010, 463( 7284): 1057 https://doi.org/10.1038/nature08814
34	Navon N. , Nascimbene S. , Chevy F. , Salomon C. . The equation of state of a low-temperature Fermi gas with tunable interactions. Science, 2010, 328( 5979): 729 https://doi.org/10.1126/science.1187582
35	L. Hung C. , Zhang X. , Gemelke N. , Chin C. . Observation of scale invariance and universality in two-dimensional Bose gases. Nature, 2011, 470( 7333): 236 https://doi.org/10.1038/nature09722
36	Yefsah T. , Desbuquois R. , Chomaz L. , J. Gunter K. , Dalibard J. . Exploring the thermodynamics of a two-dimensional Bose gas. Phys. Rev. Lett., 2011, 107( 13): 130401 https://doi.org/10.1103/PhysRevLett.107.130401
37	J. H. Ku M. , T. Sommer A. , W. Cheuk L. , W. Zwierlein M. . Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas. Science, 2012, 335( 6068): 563 https://doi.org/10.1126/science.1214987
38	Zhang X. , L. Hung C. , K. Tung S. , Chin C. . Observation of quantum criticality with ultracold atoms in optical lattices. Science, 2012, 335( 6072): 1070 https://doi.org/10.1126/science.1217990
39	C. Ha L. , L. Hung C. , Zhang X. , Eismann U. , K. Tung S. , Chin C. . Strongly interacting two-dimensional Bose gases. Phys. Rev. Lett., 2013, 110( 14): 145302 https://doi.org/10.1103/PhysRevLett.110.145302
40	Vogler A. Labouvie R. Stubenrauch F. Barontini G. Guarrera V. Ott H., Thermodynamics of strongly correlated one-dimensional Bose gases, Phys. Rev. A 88, 031603(R) ( 2013)
41	Yang B. , Y. Chen Y. , G. Zheng Y. , Sun H. , N. Dai H. , W. Guan X. , S. Yuan Z. , W. Pan J. . Quantum criticality and the Tomonaga−Luttinger liquid in one-dimensional Bose gases. Phys. Rev. Lett., 2017, 119( 16): 165701 https://doi.org/10.1103/PhysRevLett.119.165701
42	Zhang X. , Y. Chen Y. , X. Liu L. , J. Deng Y. , W. Guan X. . Interaction-induced particle−hole symmetry breaking and fractional exclusion statistics. Natl. Sci. Rev.,, 2022, nwac027 https://doi.org/10.1093/nsr/nwac027
43	P. A. Fisher M. , B. Weichman P. , Grinstein G. , S. Fisher D. . Boson localization and the superfluid−insulator transition. Phys. Rev. B, 1989, 40( 1): 546 https://doi.org/10.1103/PhysRevB.40.546
44	A. Khare, Fractional Statistics and Quantum Theory, World Scientific Publishing Co. Pte. Ltd., 5 Toh Tuck Link, Singapore 596224, 2005, Chapter 5, 2nd Ed
45	Grüter P. , Ceperley D. , Laloe F. . Critical temperature of Bose−Einstein condensation of hard-sphere gases. Phys. Rev. Lett., 1997, 79( 19): 3549 https://doi.org/10.1103/PhysRevLett.79.3549
46	H. Lieb E. , Liniger W. . Exact analysis of an interacting Bose gas (I): The general solution and the ground state. Phys. Rev., 1963, 130( 4): 1605 https://doi.org/10.1103/PhysRev.130.1605
47	W. Guan X. , T. Batchelor M. . Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. J. Phys. A Math. Theor., 2011, 44( 10): 102001 https://doi.org/10.1088/1751-8113/44/10/102001
48	Tonks L. . The complete equation of state of one, two and three-dimensional gases of hard elastic spheres. Phys. Rev., 1936, 50( 10): 955 https://doi.org/10.1103/PhysRev.50.955
49	Girardeau M. . Relationship between systems of impenetrable bosons and fermions in one dimension. J. Math. Phys., 1960, 1( 6): 516 https://doi.org/10.1063/1.1703687
50	Paredes B. , Widera A. , Murg V. , Mandel O. , Folling S. , Cirac I. , V. Shlyapnikov G. , W. Hansch T. , Bloch I. . Tonks–Girardeau gas of ultracold atoms in an optical lattice. Nature, 2004, 429( 6989): 277 https://doi.org/10.1038/nature02530
51	Kinoshita T. , Wenger T. , S. Weiss D. . Observation of a one-dimensional Tonks−Girardeau gas. Science, 2004, 305( 5687): 1125 https://doi.org/10.1126/science.1100700
52	Supporting information is available as supplementary materials.
53	G. Wilson K. . The renormalization group: Critical phenomena and the Kondo problem. Rev. Mod. Phys., 1975, 47( 4): 773 https://doi.org/10.1103/RevModPhys.47.773
54	Costello K., Renormalization and Effective Field Theory, American Mathematical Society, Providence, Rhode Island, 2011
55	Passarino G. . Veltman, renormalizability, calculability. Acta Phys. Pol. B, 2021, 52( 6): 533 https://doi.org/10.5506/APhysPolB.52.533
56	Wolf B. , Tsui Y. , Jaiswal-Nagar D. , Tutsch U. , Honecker A. , Remović-Langer K. , Hofmann G. , Prokofiev A. , Assmus W. , Donath G. , Lang M. . Magnetocaloric effect and magnetic cooling near a field-induced quantum-critical point. Proc. Natl. Acad. Sci. USA, 2011, 108( 17): 6862 https://doi.org/10.1073/pnas.1017047108
57	Y. Chen Y. , Watanabe G. , C. Yu Y. , W. Guan X. , del Campo A. . An interaction-driven many-particle quantum heat engine and its universal behavior. npj Quantum Inf., 2019, 5 : 88 https://doi.org/10.1038/s41534-019-0204-5

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