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Wang J, Pan W, Sun DY. Efficient world-line-based quantum Monte Carlo method without Hubbard-Stratonovich transformation. Sci Rep 2022; 12:8251. [PMID: 35581367 PMCID: PMC9114139 DOI: 10.1038/s41598-022-12259-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2022] [Accepted: 04/19/2022] [Indexed: 11/17/2022] Open
Abstract
By precisely writing down the matrix element of the local Boltzmann operator (\documentclass[12pt]{minimal}
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\begin{document}$${\mathrm{e}}^{-\tau h}$$\end{document}e-τh, where \documentclass[12pt]{minimal}
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\begin{document}$$h$$\end{document}h is the Hermitian conjugate pairs of off-diagonal operators), we have proposed a new path integral formulation for quantum field theory and developed a corresponding Monte Carlo algorithm. With the current formula, the Hubbard–Stratonovich transformation is not necessary, accordingly the determinant calculation is not needed, which can improve the computational efficiency. The results show that, the simulation time has the square-law scaling with system sizes, which is comparable with the usual first-principles calculations. The current formula also improves the accuracy of the Suzuki–Trotter decomposition. As an example, we have studied the one-dimensional half-filled Hubbard model at finite temperature. The obtained results are in excellent agreement with the known solutions. The new formula and Monte Carlo algorithm could be applied to various studies in future.
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Affiliation(s)
- J Wang
- Department of Physics, East China Normal University, Shanghai, 200241, China.,Shanghai Qi Zhi Institute, Shanghai, 200030, China
| | - W Pan
- Beijing Computational Science Research Center, Beijing, 100084, China
| | - D Y Sun
- Department of Physics, East China Normal University, Shanghai, 200241, China. .,Shanghai Qi Zhi Institute, Shanghai, 200030, China.
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Chen KY, Wang NN, Yin QW, Gu YH, Jiang K, Tu ZJ, Gong CS, Uwatoko Y, Sun JP, Lei HC, Hu JP, Cheng JG. Double Superconducting Dome and Triple Enhancement of T_{c} in the Kagome Superconductor CsV_{3}Sb_{5} under High Pressure. PHYSICAL REVIEW LETTERS 2021; 126:247001. [PMID: 34213920 DOI: 10.1103/physrevlett.126.247001] [Citation(s) in RCA: 73] [Impact Index Per Article: 24.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2021] [Accepted: 05/18/2021] [Indexed: 05/12/2023]
Abstract
CsV_{3}Sb_{5} is a newly discovered Z_{2} topological kagome metal showing the coexistence of a charge-density-wave (CDW)-like order at T^{*}=94 K and superconductivity (SC) at T_{c}=2.5 K at ambient pressure. Here, we study the interplay between CDW and SC in CsV_{3}Sb_{5} via measurements of resistivity, dc and ac magnetic susceptibility under various pressures up to 6.6 GPa. We find that the CDW transition decreases with pressure and experience a subtle modification at P_{c1}≈0.6-0.9 GPa before it vanishes completely at P_{c2}≈2 GPa. Correspondingly, T_{c}(P) displays an unusual M-shaped double dome with two maxima around P_{c1} and P_{c2}, respectively, leading to a tripled enhancement of T_{c} to about 8 K at 2 GPa. The obtained temperature-pressure phase diagram resembles those of unconventional superconductors, illustrating an intimated competition between CDW-like order and SC. The competition is found to be particularly strong for the intermediate pressure range P_{c1}≤P≤P_{c2} as evidenced by the broad superconducting transition and reduced superconducting volume fraction. The modification of CDW order around P_{c1} has been discussed based on the band structure calculations. This work not only demonstrates the potential to raise T_{c} of the V-based kagome superconductors, but also offers more insights into the rich physics related to the electron correlations in this novel family of topological kagome metals.
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Affiliation(s)
- K Y Chen
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - N N Wang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Q W Yin
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, China
| | - Y H Gu
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - K Jiang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Z J Tu
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, China
| | - C S Gong
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, China
| | - Y Uwatoko
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - J P Sun
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - H C Lei
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, China
| | - J P Hu
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - J-G Cheng
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
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Li ZX, Jiang YF, Yao H. Edge Quantum Criticality and Emergent Supersymmetry in Topological Phases. PHYSICAL REVIEW LETTERS 2017; 119:107202. [PMID: 28949178 DOI: 10.1103/physrevlett.119.107202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2017] [Indexed: 06/07/2023]
Abstract
Proposed as a fundamental symmetry describing our Universe, spacetime supersymmetry (SUSY) has not been discovered yet in nature. Nonetheless, it has been predicted that SUSY may emerge in low-energy physics of quantum materials such as topological superconductors and Weyl semimetals. Here, by performing state-of-the-art sign-problem-free quantum Monte Carlo simulations of an interacting two-dimensional topological superconductor, we show convincing evidence that the N=1 SUSY emerges at its edge quantum critical point (EQCP) while its bulk remains gapped and topologically nontrivial. Remarkably, near the EQCP, we find that the edge Majorana fermion acquires a mass that is identical with that of its bosonic superpartner. To the best of our knowledge, this is the first observation that fermions and bosons have equal dynamically generated masses, a hallmark of emergent SUSY. We further discuss experimental signatures of such EQCP and associated SUSY.
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Affiliation(s)
- Zi-Xiang Li
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Yi-Fan Jiang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Hong Yao
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
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Li ZX, Jiang YF, Yao H. Majorana-Time-Reversal Symmetries: A Fundamental Principle for Sign-Problem-Free Quantum Monte Carlo Simulations. PHYSICAL REVIEW LETTERS 2016; 117:267002. [PMID: 28059531 DOI: 10.1103/physrevlett.117.267002] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2016] [Indexed: 06/06/2023]
Abstract
A fundamental open issue in physics is whether and how the fermion sign problem in quantum Monte Carlo (QMC) simulations can be solved generically. Here, we show that Majorana-time-reversal (MTR) symmetries can provide a unifying principle to solve the fermion sign problem in interacting fermionic models. By systematically classifying Majorana-bilinear operators according to the anticommuting MTR symmetries they respect, we rigorously prove that there are two and only two fundamental symmetry classes which are sign-problem-free and which we call the "Majorana class" and "Kramers class," respectively. Novel sign-problem-free models in the Majorana class include interacting topological superconductors and interacting models of charge-4e superconductors. We believe that our MTR unifying principle could shed new light on sign-problem-free QMC simulation on strongly correlated systems and interacting topological matters.
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Affiliation(s)
- Zi-Xiang Li
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Yi-Fan Jiang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Hong Yao
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
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Zaanen J, Overbosch BJ. Mottness collapse and statistical quantum criticality. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2011; 369:1599-1625. [PMID: 21422017 DOI: 10.1098/rsta.2010.0188] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We put forward here the case that the anomalous electron states found in cuprate superconductors and related systems are rooted in a deeply non-classical fermion sign structure. The collapse of Mottness, as advocated by Phillips and supported by recent dynamical cluster approximation results on the Hubbard model, sets the necessary microscopic conditions. The crucial insight is due to Weng, who demonstrated that, in the presence of Mottness, the fundamental workings of quantum statistics change, and we will elaborate on the effects of this Weng statistics with an emphasis on characterizing it further using numerical methods. The pseudo-gap physics of the underdoped regime appears as a consequence of the altered statistics and the profound question is how to connect this by a continuous quantum phase transition to the overdoped regime ruled by normal Fermi-Dirac statistics. Proof of principle follows from Ceperley's constrained path integral formalism, in which states can be explicitly constructed showing a merger of Fermi-Dirac sign structure and scale invariance of the quantum dynamics.
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Affiliation(s)
- J Zaanen
- Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, PO Box 9506, 2300 RA Leiden, The Netherlands
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Lacy JW, Yassa MA, Stark SM, Muftuler LT, Stark CE. Distinct pattern separation related transfer functions in human CA3/dentate and CA1 revealed using high-resolution fMRI and variable mnemonic similarity. Learn Mem 2011; 18:15-8. [PMID: 21164173 PMCID: PMC3023966 DOI: 10.1101/lm.1971111] [Citation(s) in RCA: 261] [Impact Index Per Article: 20.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2010] [Accepted: 10/10/2010] [Indexed: 11/25/2022]
Abstract
Producing and maintaining distinct (orthogonal) neural representations for similar events is critical to avoiding interference in long-term memory. Recently, our laboratory provided the first evidence for separation-like signals in the human CA3/dentate. Here, we extended this by parametrically varying the change in input (similarity) while monitoring CA1 and CA3/dentate for separation and completion-like signals using high-resolution fMRI. In the CA1, activity varied in a graded fashion in response to increases in the change in input. In contrast, the CA3/dentate showed a stepwise transfer function that was highly sensitive to small changes in input.
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Affiliation(s)
- Joyce W. Lacy
- Center for the Neurobiology of Learning and Memory, Department of Neurobiology and Behavior, University of California, Irvine, Irvine, California 92697, USA
| | - Michael A. Yassa
- Center for the Neurobiology of Learning and Memory, Department of Neurobiology and Behavior, University of California, Irvine, Irvine, California 92697, USA
| | - Shauna M. Stark
- Center for the Neurobiology of Learning and Memory, Department of Neurobiology and Behavior, University of California, Irvine, Irvine, California 92697, USA
| | - L. Tugan Muftuler
- Department of Radiological Sciences, Center for Functional Onco Imaging, University of California, Irvine, California 92697, USA
| | - Craig E.L. Stark
- Center for the Neurobiology of Learning and Memory, Department of Neurobiology and Behavior, University of California, Irvine, Irvine, California 92697, USA
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Čubrović M, Zaanen J, Schalm K. String Theory, Quantum Phase Transitions, and the Emergent Fermi Liquid. Science 2009; 325:439-44. [DOI: 10.1126/science.1174962] [Citation(s) in RCA: 345] [Impact Index Per Article: 23.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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