Imaginärzeit-Instantonen und Pseudogap-Zustände in supraleitenden Cupraten.
Zusammenfassung der Projektergebnisse
The analysis of symmetries and of the spontaneous symmetry breaking is the cornerstone of the modern physics. Among the most fundamental symmetries, one can list the spatial translational and time translational symmetries. The spatial translational symmetry can be spontaneously broken which leads to the formation of crystals. On the other hand, the Special Theory of Relativity implies that the time and space should be treated on the equal footing, which naturally leads to the question: can time-translational symmetry also be spontaneously broken? Such a state could be by analogy called Time Crystal and would be characterized by non-trivial non-decaying oscillations of the order parameter correlation function even at asymptotically large times. This question precisely was posed by F. Wilczek [1] in 2012 which led to the active study of Time Crystals, however it was quickly realized that such a state is problematic, and in 2015 Watanabe and Oshikawa [2] showed that spontaneous breaking of continuous time-translational symmetry is impossible in practice. Since then, the community focused on the spontaneous symmetry breaking of discrete time-translational symmetry in periodically driven systems [3] that was not ruled out by the ”no-go” theorem of Watanabe and Oshikawa. There was however another largely unexplored alternative, i.e., that of the ”Imaginary Time Crystals”, which was independently proposed and developed in the works of Mukhin [4, 5, 6, 7]. In the condensed matter setting, the properties of a system at equilibrium can be described by a Euclidean Field Theory [8] where the role of time is played by imaginary time τ . To be more precise, focusing on the ordered state of the system, the partition function governing thermodynamic properties can be written in the form of the functional integral over bosonic order parameter field Z= D[∆(⃗, τ )]e−S[∆(⃗,τ )] , r r r r where imaginary time 0 ⩽ τ < 1/T and the order parameter field is periodic ∆(⃗, τ +1/T ) = ∆(⃗, τ ). Neglecting the fluctuations, the functional integral can be related to the saddle point of the action r S[∆(⃗, τ )]. The idea of the Imaginary Time Crystal is then to have the saddle point corresponding to a nontrivial oscillating order parameter configuration ∆(⃗, τ ) ̸≡ const. Realization of the Imaginary r Time Crystal and the study of its properties was the main goal of the project. In the course of the project, as our main playground, we focused on the Spin-Fermion Model with Overlapping Hotspots (SFMOH), a variation of the original Spin-Fermion model [9] developed previously [10, 11, 12] by the Konstantin Efetov in the context of cuprate physics. One of the important features of the SFMOH is that it naturally hosts the D-density wave (DDW) state — a candidate state for the explanation of pseudogap physics in Cuprates [13]. For example, such state leads to a reconstructed Fermi surface consistent with the transport [14, 15] and ARPES [16] signatures of the pseudogap. In addition to that, the state breaks the Time-reversal symmetry and its modified version can explain the observation of polar Kerr effect [17]. On the other hand, DDW state must lead to the appearance of (π, π)-peak in the polarized elastic neutron scattering, which is not observed in experiments [18, 19, 20, 21]. The DDW state corresponds to the static configuration of bond currents organized in alternating loops. It is characterized by a real order parameter corresponding to the Z2 broken symmetry. In [c], we have considered the DDW state in the context of SMOFH and proposed to couple original fermionic degrees of freedom to the additional bosonic degrees of freedom in such a way, as to induce the additional non-local in imaginary-time repulsion in the loop current order parameter. We have demonstrated, that in such model the original DDW becomes energetically unfavourable in comparison with another state that we called Instanton Crystal. Instanton Crystal is characterized by the mean-field non-static order parameter configuration, that takes the form of the train of alternating instantons and antiinstantons (configurations, connecting the two degenerate ground states of the DDW order). What is important, the order parameter in the Instanton Crystal state is averaged to zero due to oscillations, which physically corresponds to the vanishing of the static configuration of the loop bond currents and hence to the vanishing of the (π, π) peak in the polarized elastic neutron scattering. In [d], we considered the time-autocorrelation function of the order parameter in the Instanton Crystal state, which we showed to be physically related to the polarized inelastic neutron scattering cross-section at (π, π). We computed this correlation function in the mean-field approximation and showed that it exhibits slowly-decaying non-trivial oscillations, reminiscent of prethermal Time Crystals [3].
Projektbezogene Publikationen (Auswahl)
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Mean-field thermodynamic quantum time-space crystal: Spontaneous breaking of time-translation symmetry in a macroscopic fermion system. Physical Review B, 100(24).
Efetov, Konstantin B.
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Order Parameter in Electron System: Its Fluctuations and Oscillations. Journal of Experimental and Theoretical Physics, 129(4), 680-692.
Efetov, K. B.
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Phase transition into an instanton crystal state. Physical Review B, 103(7).
Starkov, Grigory A. & Efetov, Konstantin B.
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Slowly decaying real-time oscillations in instanton crystals. Physical Review B, 105(15).
Starkov, Grigory A. & Efetov, Konstantin B.
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Formation of exceptional points in pseudo-Hermitian systems. Physical Review A, 108(2).
Starkov, Grigory A.; Fistul, Mikhail V. & Eremin, Ilya M.
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Quantum phase transitions in non-Hermitian T-symmetric transverse-field Ising spin chains. Annals of Physics, 456, 169268.
Starkov, Grigory A.; Fistul, Mikhail V. & Eremin, Ilya M.
