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arXiv:2106.05383 · physica status solidi (b)

The Extended Diffusive Sachdev–Ye–Kitaev Model as a Sort of “Strange Metal”

A. Tagliacozzo

Published Dec 18, 2021• 1 citation
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Abstract

The linear dependence on temperature of the resistivity in metals undergoing high‐temperature superconducting transition is a puzzle, which is generally attributed to non‐Fermi liquid behavior on a large range of temperature values. No particle and momentum conservation characterizes the 0 + 1 − d Sachdev–Ye–Kitaev model as a tractable non‐Fermi liquid starting paradigm, when extended to higher space dimensions. Due to the conformal symmetry breaking in the incoherent phase, Goldstone bosons arise, which provide energy diffusion in the lattice. The linear response to energy diffusion in the model is discussed, which is in principle charge neutral and non‐momentum conserving, and the temperature dependence of the thermal and electric conductivity in the incoherent prechaotic, intermediate temperature phase is obtained.

DOI
10.1002/pssb.202100271

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The linear dependence on temperature of the resistivity in metals undergoing high‐temperature superconducting transition is a puzzle, which is generally attributed to non‐Fermi liquid behavior on a large range of temperature values. No particle and momentum conservation characterizes the 0 + 1 − d Sachdev–Ye–Kitaev model as a tractable non‐Fermi liquid starting paradigm, when extended to higher space dimensions. Due to the conformal symmetry breaking in the incoherent phase, Goldstone bosons arise, which provide energy diffusion in the lattice. The linear response to energy diffusion in the model is discussed, which is in principle charge neutral and non‐momentum conserving, and the temperature dependence of the thermal and electric conductivity in the incoherent prechaotic, intermediate temperature phase is obtained.
Models for strongly interacting fermions in disordered clusters forming an array, with electron hopping between sites, reproduce the linear dependence on temperature of the resistivity, typical of the strange metal phase of high temperature superconducting materials [extended Sachdev-Ye-Kitaev (SYK) models]. We identify the low energy collective excitations as neutral energy excitations, diffusing in the lattice of the thermalized non-Fermi liquid phase. However, the diffusion is heavily hindered by coupling to the pseudo-Goldstone modes of the conformal broken symmetry SYK phase, which are local in space. The imaginary time evolution of the extended model in the strong interaction and 1/N1/N1/N expansion limit is presented in the incoherent nonchaotic regime. On the other hand, a Fermi electronic liquid at low energy becomes marginal when perturbed by the SYK dots. A critical temperature for superconductivity is derived, which is not BCS-like, in case the collective excitations are assumed to mediate an attractive Cooper pairing.
Models for strongly interacting fermions in disordered clusters forming an array, with electron hopping between sites, reproduce the linear dependence on temperature of the resistivity, typical of the strange metal phase of High Temperature Superconducting materials (Extended Sachdev-Ye-Kitaev (SYK) models). Our hydrodynamical approach to the marginal Fermi liquid emerging out of the interaction, identifies the low energy collective excitations of the system in its coherent phase. These neutral excitations diffuse in the lattice, but the diffusion is heavily hindered by coupling to the pseudo Goldstone modes of the conformal broken symmetry SYK phase, which are local in space. A critical temperature for superconductivity arises in the electron liquid,in case these excitations are assumed to mediate an attractive Cooper-pairing, in the electron liquid, which is not BCS-like.
Prominent systems like the high-T_{c} cuprates and heavy fermions display intriguing features going beyond the quasiparticle description. The Sachdev-Ye-Kitaev (SYK) model describes a (0+1)D quantum cluster with random all-to-all four-fermion interactions among N fermion modes which becomes exactly solvable as N→∞, exhibiting a zero-dimensional non-Fermi-liquid with emergent conformal symmetry and complete absence of quasiparticles. Here we study a lattice of complex-fermion SYK dots with random intersite quadratic hopping. Combining the imaginary time path integral with real time path integral formulation, we obtain a heavy Fermi liquid to incoherent metal crossover in full detail, including thermodynamics, low temperature Landau quasiparticle interactions, and both electrical and thermal conductivity at all scales. We find linear in temperature resistivity in the incoherent regime, and a Lorentz ratio L≡(κρ/T) varies between two universal values as a function of temperature. Our work exemplifies an analytically controlled study of a strongly correlated metal.
Despite considerable theoretical effort, there has been no consensus on the description of the strange metal state seen in high temperature superconductors and its linear in T resistivity. Here, we construct a simple solvable model of itinerant electrons interacting through random couplings on a honeycomb lattice composed of Sachdev-Ye-Kitaev quantum dots which describes electrons without quasiparticle excitations. This model is solvable in the large-N limit and displays a temperature dependant crossover between two regimes. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite T crossover to a fully incoherent regime that also has a linear in T resistivity. In the non-Fermi liquid regime, the dc resistivityincreases linearly with temperature over a broad range of temperatures. The self energy has a singular frequency dependence but lacks momentum dependence which is reminiscent of a dynamical mean-field-theory-like behavior but in dimensions d < ∞ . In the low-temperature and strong-coupling limit, the behaviour parallels that of Dirac fermions. We discuss the implications of theseresults and further possibilities in such studies.
"Strange metals" with resistivity depending linearly on temperature T down to low T have been a long-standing puzzle in condensed matter physics. Here, we consider a lattice model of itinerant spin-[Formula: see text] fermions interacting via onsite Hubbard interaction and random infinite-ranged spin-spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behavior, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-M limit of [Formula: see text] symmetric models to models with physical [Formula: see text] spin-[Formula: see text] electrons. Remarkably, the quantum critical regime also features a Planckian linear-T resistivity associated with a T-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the marginal Fermi liquid phenomenology.
Some of the most interesting phenomena in condensed matter occur in high-temperature superconductors and heavy fermions, and arise from a parent non-Fermi-liquid background. Although the non-Fermi-liquid phase has metallic character, it is very different from typical metals in that the electronic excitations are not particlelike (no quasiparticles), and this has lead to these phases eluding a clear theoretical description. Here, the authors develop a model that provides a route to describe non-Fermi liquids realized in condensed matter systems. Building on the zero-dimensional Sachdev-Ye-Kitaev model that is inspired by connections between a non-Fermi liquid and black holes, the authors construct a model in a lattice system where the bands touch to give a divergent density of states (Lifshitz point). The resulting non-Fermi-liquid phases exhibit intriguing properties such as scaling symmetry, nontrivial power-law dependence of entropy on temperature, and fast information scrambling with rate linear in temperature, as well as dynamical transitions to more conventional phases with well-defined quasiparticles.