Instanton Sector of Correlated Electron Systems as the Origin of Populated Pseudo-gap and Flat “Band” Behavior: Analytic Solution

Abstract

Finite temperature instantons between meta-stable vacua of correlated electronic system are solved analytically for quasi one-dimensional Hubbard model. The instantons produce dynamic symmetry breaking and connect metallic state with the dual vacua: superconducting (SC) and spin-density wave (SDW) states. The instantons spread along the Matsubara's imaginary time and possess the structure similar to the coordinate-space solitonic lattices previously discovered in quasi one-dimensional Peierls model. On the microscopic level the inter-vacua excursion is described by mutual transformations between the "resonating quartets" of the couples of electron-hole and Cooper pairs. Spectral properties of the electrons in the "instantonic crystal" reveal pseudo-gap (PG) behavior, with finite fermionic density of states in the center of the PG and "flat-band" outside of it. Analytically derived inverse temperature scaling of the pseudo-gap and the densities of the SC and SDW condensates is discussed in the context of ARPES and STM data in high-Tc cuprates.It is for long time now that competing orders are considered as one of the core properties of underdoped high-T c cuprates [1], [2]. Nevertheless, the nature of the non-superconducting order remains a mystery. Especially challenging is the pseudo-gap (PG) phenomenon observed in high-T c cuprates [3]. Here we study a novel possibility, which exploits a well known concept of highenergy physics, an instanton, that connects vacua of the many-body system possessing different symmetries [4]. The instanton sector of the Hilbert space of the manybody system is known to possess dynamically generated masses of the excitations in the system [4]. We find that this mechanism in the correlated electron system has interesting peculiarity: the "mass" is acquired by fermionic Landau quasi-particles inside the pseudo-gap, but neither right in its center, nor far away from the PG region of the spectrum. In the center of the pseudo-gap the quasiparticle dispersion remains linear in momentum ("relativistic"), but acquires just strong enhancement of the Fermi velocity. Outside the PG region the spectrum remains not renormalized. As a result, in the cross-over region a "flat band" forms in the fermionic excitation spectrum, see Figs. 1,2, with a weaker dependence on momentum. We demonstrate these properties using a (quasi) one-dimensional model of electron system, which is especially convenient tool for understanding the major effects that occur, since it proves to be analytically solvable and, hence, provides in-depths information. We also discuss predicted measurable characteristics of the electronic system that undergoes symmetry excursions into the (dual) meta-stable vacua described respectively with superconducting (SC) and spin-density wave (SDW) orders. These vacua are chosen as the most relevant ones since ARPES, STM and INS experiments [3,5,6,7,8] reveal PG behavior in the anti-nodal region of the Fermi surface of doped high-T c cuprates with coexisting magnetic and superconducting fluctu...

Order Parameter in Electron Systems: Its Fluctuations and Oscillations

“…The existence of the non-trivial local minima F [b, 0], Eq. (43), at b 0 (τ ) has been established previously by Mukhin [74][75][76] starting from a different model. Generally, there can be many solutions corresponding to different minima of F [b, 0] depending on ЖЭТФ Order parameter in electron systems: its fluctuations and oscillations the number m of instanton-antiinstanton pairs (IAP).…”

Thermodynamic Quantum Time Crystals

“…Existence of the non-trivial local minima (11) of F [b, 0] at b 0 (τ ) has been established previously by Mukhin [40,41] starting from a different model. Generally, there can be many solutions corresponding to different minima of F [b, 0] depending on the number m of instantonantiinstanton pairs (IAP).…”

Imaginary time crystal of thermal quantum matter

“…The nature of this phase can be qualitatively understood in the strong coupling limit α ≫ J, where the retarded interaction dominates in the partition function. For each site, the retarded interaction (3) favors configurations with alternating n(τ ) that oscillates between 0 and 1 with a frequency 2πω c , which is reminiscent of the soliton solutions in the BCS pairing model [26,27], similar states have recently been proved to be metastable in a wide class of closed quantum many-body systems [28]. Since a world line needs to be continuous, the temporal-spatial configurations minimizing the retarded interacting action (2) are highly degenerate.…”