当一个系统由一个大的子系统（热库）和一个小的子系统（探针）组成时，热化意味着将热库的温度传递给探针。如果热库和探针都由相同的微观哈密顿量描述，热化进一步意味着探针吸收热库的相位。我们将这种现象称为“相位热化”。然而，当探针和热库由不同的微观哈密顿量描述时，这种现象是否可实现尚不清楚。我们证明，即使微观哈密顿量显著不同，相位热化也是可能的。我们给出一个明确的例子，其中探针是由一条 Majorana 链实现的费米液体，每个格点有 n ≫ 1 个费米子，通过随机跃迁相互作用；热库是由另一条 Majorana 链描述的非相干金属，每个格点有 N > n 个费米子，通过任意长程随机四费米子相互作用。在深红外（即在非常低的能量下），探针转变为非相干金属，其 Lyapunov 谱和扩散系数与热库相同。
英文摘要：
When a system consists of a large subsystem (bath) and a small one (probe), thermalization implies induction of temperature of the bath onto the probe. If both the bath and the probe are described by same microscopic Hamiltonian, thermalization further entails that the probe imbibes the phase of the bath. We refer to this phenomenon as {\it phase thermalization}. However, it is not clear whether this phenomenon is realizable when the probe and the bath are described by different microscopic Hamiltonians. We show {\it phase thermalization} is possible even when the microscopic Hamiltonians differ significantly. We provide an explicit example, where the probe is a Fermi liquid realized by a Majorana chain with $n \gg 1$ fermions per site interacting through random hopping and the bath is an incoherent metal described by another Majorana chain with $N > n$ fermions per site interacting through arbitrarily long range random four-fermion interaction. In deep infrared (\emph{i.e.} at very low energies), the probe turns into an incoherent metal, with Lyapunov spectrum and diffusion coefficient identical to the bath.
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Abstract We study a two-band dispersive Sachdev-Ye-Kitaev (SYK) model in 1 + 1 dimension. We suggest a model that describes a semimetal with quadratic dispersion at half-filling. We compute the Green's function at the saddle point using a combination of analytical and numerical methods. Employing a scaling symmetry of the Schwinger-Dyson equations that becomes transparent in the strongly dispersive limit, we show that the exact solution of the problem yields a distinct type of non-Fermi liquid with sublinear $ρ\propto T^{2/5}$ temperature dependence of the resistivity. A scaling analysis indic…
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Marginal Fermi-liquid physics near optimal doping in high T_{c} cuprates has been explained within two competing scenarios such as the spin-fluctuation theory based on an itinerant picture and the slave-particle approach based on a localized picture. In this study we propose an alternative scenario for the anomalous transport within the context of the slave-particle approach. Although the marginal Fermi-liquid phenomenology was interpreted previously within deconfinement of the compact gauge theory, referred to as the strange metal phase, we start from confinement, introducing the Polyakov-loo…
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We consider the interaction-driven Mott transition at zero temperature from the viewpoint of microscopic Fermi liquid theory. To this end, we derive an exact expression for the Landau parameters within the dynamical mean-field theory (DMFT) approximation to the single-band Hubbard model. At the Mott transition the symmetric and the anti-symmetric Landau parameter diverge. The vanishing compressibility at the Mott transition directly implies the divergence of the forward scattering amplitude in the charge sector, which connects the proximity of the Mott phase to a tendency towards phase separat…
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We study the dynamics of a quantum system in thermal equilibrium that is suddenly coupled to a bath at a different temperature, a situation inspired by a particular black hole evaporation protocol. We prove a universal positivity bound on the integrated rate of change of the system energy which holds perturbatively in the system-bath coupling. Applied to holographic systems, this bound implies a particular instance of the averaged null energy condition. We also study in detail the particular case of two coupled SYK models in the limit of many fermions using the Schwinger-Keldysh non-equilibriu…
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Sr$_2$IrO$_4$ is the archetype of the spin-orbit Mott insulator, but the nature of the metallic states that may emerge from this type of insulator is still not very well known. We study with angle-resolved photoemission the insulator-to-metal transition observed in Sr$_2$Ir$_{1-x}$Rh$_x$O$_4$ when Ir is substituted by Rh (0.02 < $x$ < 0.35). The originality of the Rh doping is that Ir and Rh, which are formally isovalent, adopt different charge states, a rather unusual and inhomogeneous situation. We show that the evolution to the metallic state can be essentially understood as a shift of the …
The shear viscosity is an important characterization of how a many-body system behaves like a fluid. We study the shear viscosity in a strongly interacting solvable model, consisting of coupled Sachdev-Ye-Kitaev (SYK) islands. As temperature is lowered, the model exhibits a crossover from an incoherent metal with local criticality to a marginal fermi liquid. We find that while the ratio of shear viscosity to entropy density in the marginal Fermi liquid regime satisfies a Kovtun-Son-Starinets (KSS) like bound, it can strongly violate the KSS bound in a robust temperature range of the incoherent…
Strongly correlated metals comprise an enduring puzzle at the heart of condensed matter physics. Commonly a highly renormalized heavy Fermi liquid occurs below a small coherence scale, while at higher temperatures a broad incoherent regime pertains in which quasi-particle description fails. Despite the ubiquity of this phenomenology, strong correlations and quantum fluctuations make it challenging to study. The Sachdev-Ye-Kitaev(SYK) model describes a $0+1$D quantum cluster with random all-to-all \emph{four}-fermion interactions among $N$ Fermion modes which becomes exactly solvable as $N\righ…
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In unconventional superconductors, it is generally believed that understanding the physical properties of the normal state is a pre-requisite for understanding the superconductivity mechanism. In conventional superconductors like niobium or lead, the normal state is a Fermi liquid with a well-defined Fermi surface and well-defined quasipartcles along the Fermi surface. Superconductivity is realized in this case by the Fermi surface instability in the superconducting state and the formation and condensation of the electron pairs (Cooper pairing). The high temperature cuprate superconductors, on…
We study the non-equilibrium dynamics of a Luttinger liquid after a simultaneous quantum quench of the interaction and dissipative quench to the environment within the realm of the Lindblad equation. When the couplings to environment satisfy detailed balance, the system is destined to thermalize, which we follow using bosonization. The thermodynamic entropy of the system, which also encodes information about the entanglement with the environment, either exhibits a maximum and minimum or grows monotonically before reaching its thermal value in a universal fashion. The single-particle density ma…
Good metals are characterised by diffusive transport of coherent quasi-particle states and the resistivity is much less than the Mott-Ioffe-Regel (MIR) limit, $\frac{ha}{e^{2}}$, where $a$ is the lattice constant. In bad metals, such as many strongly correlated electron materials, the resistivity exceeds the Mott-Ioffe-Regel limit and the transport is incoherent in nature. Hartnoll, loosely motivated by holographic duality (AdS/CFT correspondence) in string theory, recently proposed a lower bound to the charge diffusion constant, $D \gtrsim \hbar v_{F}^{2}/(k_{B}T)$, in the incoherent regime o…
