Session G30: Strongly Correlated Systems, Including Quantum Fluids and Solids VI

The Frustration of Being Odd

We consider the effects of so-called Frustrated Boundary Conditions (FBC) on quantum spin chains, namely periodic BC with an odd number of sites. In absence of external fields, FBC allow for the direct determination of correlation functions that signal a spontaneous symmetry breaking, such as the spontaneous magnetization. When paired with anti-ferromagnetic interactions, FBC introduce geometrical frustration into the system and the ground state develops properties which differ from those present with other boundary conditions, such as the disappearance of the usual order, possibly replaced by different ones. We argue that FBC introduce a fractionalized excitation that contributes to long-range order in the system, similar to that enjoyed by SPT phases. Our results prove that even the weakest form of geometrical frustration can deeply affect a system's properties and pave a way for a bottom-up approach to better understand the effects of frustration and their exploitations also for technological purposes.

    

Emergent gauge fields in holographic strange metals

Using gauge/gravity duality, strange metallic phases with non-trivial temperature scalings of eg the resistivity are obtained from black hole spacetimes with an emergent critical infrared geometry. In this talk, I will argue that they are described by an effective field theory of gapless bosonic fields coupled to emergent, non-local gauge fields. I will comment on the relation to the Luttinger theorem and the presence of fractionalized charged degrees of freedom.   

Large N theory of critical Fermi surfaces II: conductivity

A Fermi surface coupled to a scalar field can be described in a 1/N expansion by choosing the fermionscalar Yukawa coupling to be random in the N-dimensional flavor space, but invariant under translations. We compute the conductivity of such a theory in two spatial dimensions for a critical scalar. We find a Drude contribution, and verify that the proposed 1/ω^2/3 contribution to the optical conductivity at frequency ω has vanishing co-efficient for a convex Fermi surface. We also describe the influence of impurity scattering of the fermions, and find that while the self energy resembles a marginal Fermi liquid, the resistivity and optical conductivity behave like a Fermi liquid.   

Molecular beam epitaxy growth of correlated kagome metal Ni3In

The past few years have seen a rapid development in material realizations of the kagome lattice model and its derived band structure singularities. A bulk single crystal study of an AB-stacked kagome metal Ni₃In has identified an emergent d-electron flat band associated with non-Fermi liquid behavior, understood to arise from the inter-kagome hybridization in its characteristic three-dimensional stacking network of kagome layers [1]. Here we report the stabilization of high quality epitaxial thin films of Ni₃In by molecular beam epitaxy [2]. Based on the electrical transport response, we discuss the relevance of spin fluctuations in generating the observed correlated behaviors. We will also propose various thin film engineering strategies for controlling the lattice-driven quantum criticality.

    

Solvable Models of non-Fermi liquids with non-trivial bandstructure

Motivated by recent experimental studies in correlated materials with non-Fermi liquid behavior and extra local degrees of freedom, we construct minimal solvable models of a non-Fermi liquid with non-trivial band structure such as flat bands or band-inversions. These models rely on higher-dimensional extensions of the Sachdev-Ye-Kitaev (SYK) model. Typical lattice generalizations of the SYK model cross over to a Fermi liquid at low-temperatures. Notable exceptions consist of models with divergent density of Bloch states. We investigate the role that increased density of states arising naturally from band-touching points and flat-bands can have on this nFL-FL crossover. We also examine the effect these considerations have on various symmetry-broken resulting phases. Analytic and numerical techniques are used to explore the interplay of various forms of SYK-type interactions with novel band structures, and their resulting transport properties.   

Thermal radiation from molecular chains in ultra-strong magnetic fields

Magnetic fields exceeding 10^{12} G exist at the surface of certain neutron stars and magnetars. In such fields, atomic structure is fundamentally altered, allowing for the formation of long molecular chains. These chains may dominate the emission properties of certain stars. In this talk, we present recent theoretical work on the spectra and polarization structure of the radiation emitted from these chains. We find that accounting for electron-electron interactions is essential, and our theory makes extensive use of the Tomonaga-Luttinger liquid model. The radiation is composed of discrete and continuous components, and its non-universal form offers signatures of the composition of the chains as well as the ambient magnetic field.   

Unconventional Superconductivity from Fermi Surface Fluctuations in Strongly Correlated Metals

The mechanism for unconventional superconductivity in quantum critical metals remains a puzzle in the field of strongly correlated systems. The notion of a Kondo destruction quantum critical point, at which quasiparticles are lost everywhere on the Fermi surface and across which Fermi surface goes from large to small, has been advanced in the study of antiferromagnetic heavy-fermion metals [1].  Here [2], using the cluster EDMFT method [3], we demonstrate how the Fermi surface fluctuations drive unconventional superconductivity whose transition temperature is exceptionally high relative to (reaching several percent of) the effective Fermi temperature. Our results provide a natural understanding of the enigmatic superconductivity in a host of heavy-fermion metals. Moreover, the qualitative physics underlying our findings and their implications for the formation of unconventional superconductivity apply to other highly correlated metals with strong Fermi-surface fluctuations.

 

[1] S. Paschen and Q. Si, Nat. Rev. Phys. 3, 9 (2021). Q. Si et al, Nature 413, 804 (2001); S. Kirchner et al, Rev. Mod. Phys. 92, 011002 (2020).

 

[2] H. Hu, et al., arXiv:2109.13224 (2021).

 

[3] J. Pixley et al, PRB 91, 125127 (2015).

 

    

Counting statistics in interacting one-dimensional conductors

The calculation of the cumulant generating function of a given observable, such as the charge, is nontrivial even for the non-interacting systems. This problem is closely connected to the problem of Toeplitz eigenvalues and the Szego-Kac theorem [1]. The application of the latter in zero temperature case leads to a) violation of the moment generating function's periodicity along the counting field b) matrix size cutoff in the logarithmic divergent terms. The periodicity can be restored using the Fisher-Hartwig conjecture, as was shown for non-interacting one-dimensional electrons [2,3]. Here, we aim to go beyond and include interactions. For weak interactions we developed a modification of the Matsubara diagrammatic approach, which allows us an explicit calculation of the interaction corrections to the cumulant generating function. All obtained terms preserve the periodic constraint of the moment generating function. The obtained result is in a good agreement at low filling with the noise suppression in Luttinger liquid for K<1, moreover, we are able to determine quantitively the infrared cutoff in noise terms as well as its dependence on parameter K. We also found a surprising counterpart of the charge-density wave effect in the cumulant generating function.   

Emergent nodal non-Fermi liquid behavior from a Berry dipole

The study of topological phases has been an intriguing area of research in condensed matter physics for over a decade. In this work, we investigate the effects of long-range Coulomb interaction at the topological quantum critical point (TQCP) between a Hopf insulator and a trivial insulator. At the TQCP, the band-crossing point realizes a Berry dipole [1], and fermionic states in its vicinity strongly couple with the Coulomb field. Using perturbative renormalization group methods, we identify that the Coulomb interaction drives the system into a new type of quasiparticleless critical state [2]. The nodal non-Fermi liquid, thus obtained, controls finite temperature behaviors over a wide region of the phase diagram.  We derive the associated scaling behaviors of various observables, and explore possible experimental realizations.

 [1] A. Nelson, et al., Phys. Rev. B 106, 075124 (2022)

 [2] K. Ladovrechis and S. Sur, (to appear)   

Quantum Oscillations beyond the Onsager relation in a doped Mott insulator

The kinetic energy of electrons in a magnetic field is quenched resulting in a discrete set of highly degenerate Landau levels (LL). This gives rise to fascinating phenomena like quantum oscillations or the integer and fractional quantum Hall effect. The latter is a result of interactions partially lifting the degeneracy within a given LL while inter-LL interactions are usually assumed to be unimportant. Here, we study the LL spectrum of the Hatsugai-Kohmoto model, a Hubbard-like model which is exactly soluble on account of infinite range interactions. For the doped Mott insulator phase in a magnetic field we find that the degeneracy of LLs is preserved but inter-LL interactions are important leading to a non-monotonous reconstruction of the spectrum. As a result, strong interactions lead to aperiodic quantum oscillations of the metallic phase in contrast to Onsager's famous relation connecting oscillation frequencies with the Fermi surface areas at zero field. In addition, we find unconventional temperature dependencies of quantum oscillations and effective mass renormalizations. We discuss the general importance of inter-LL interactions for understanding doped Mott insulators in magnetic fields.   

Magnetotransport Measurement of Mesoscale Thin-film Strange Metal Sr3Ru2O7 Structures

Sr₃Ru₂O₇ (SRO327) is a material that, in the bulk, exhibits a strange metal phase via tuning of the magnetic field to a quantum critical point <!--[if gte msEquation 12]> style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
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normal'>H_c~7.8H_c ∼ 7.8 T. Fabrication of thin filmed SRO327 allows access to mesoscale measurements of the strange metal phase reported in bulk samples. Initial magnetotransport measurements of nanowires patterned from SRO327 can confirm quality and robustness of the fabrication process through comparison with unpatterned larger areas of the film. Further measurements via shot noise offer a look at the nature of charge carriers in the strange metal when compared to the normal metal phase.   

Superconductivity from an incoherent metal in a Yukawa Sachdev-Ye-Kitaev model

Superconductivity emerging out of strongly correlated metal has been a topic of great interest in recent years. A popular class of theories for the onset of superconductivity from a strange metal focus on a normal state which has a Fermi surface coupled to a critical boson. Motivated by a SYK-inspired large N theory of a sharp Fermi surface in two spatial dimensions, we analyze instabilities towards superconducting pairing from an incoherent normal state. We calculate the superconducting transition and other properties of the superconductor, and finally discuss the interplay between superconductivity and a "Planckian" normal state resistivity.   

Quantum Criticality in Kondo Lattice Model: A Renormalization Group Study Via Quantum non-Linear Sigma Model

When quasiparticles in a metal interact by exchanging soft collective modes, their dynamics tend to develop singularities which, if sufficiently strong, may even destroy the quasiparticle-coherence. The possibility of such quasiparticleless metallic states has long motivated theoretical and experimental investigations into itinerant systems at the edge of quantum phase transitions. Since heavy-fermion metals naturally possess the two necessary components, itinerant electrons and fluctuating local moments, they have played a key role in shaping our understanding of quantum critical metals [1]. Here, we study the antiferromagnet- to-paramagnet transition of a Kondo lattice model. We assess the effect of Kondo coupling through a renormalization group analysis. Our results shed new light on the global phase diagram of the heavy fermion systems [2] and, especially, the behavior of frustrated Kondo lattice[3,4].

[1] S. Paschen & Q. Si, Nat. Rev. Phys. 3, 9-26 (2021); S. Kirchner et al, RMP. 92, 011002 (2020); Q. Si et al., Nature 413, 804 (2001)

[2] Q. Si, Physica B378, 23 (2006); Phys. Status Solidi B 247, 476 (2010).

[3] H. Zhao et al, Nat. Phys. 15, 1261 (2019).

[4] M. Kavai et al, Nat. Comm. 12, 1377 (2021).

    

RG flow of the coupling functions around the Fermi liquid phase

In this work, we propose a new functional renormalization group (RG) method for the fermi liquid phase. Instead of the coupling constants, we study the flow of coupling functions parametrized by the angle of Fermi momenta. Particularly, we consider the nearly forward scattering and nearly backward scattering respectively. Different from the forward scattering which is exactly marginal, the nearly forward scattering can induce RG flow towards the Fermi liquid. The RG flow is traced back to an unstable fixed point which describes the transition between the Fermi liquid and the Ising nematic phase. The critical theory has been studied before as a non-Fermi liquid. For the first time, we are able to give a RG formulation for the Pomeranchuk instability which has been studied for a long time. Besides, by studying the nearly backward scattering, we find a new fixed point separating Fermi liquid and superconductor at 2+epsilon spatial dimension. It is described by a critical theory distinct from the Ising nematic transition. Therefore, this generalized RG method focusing on the flow of coupling functions opens a new route towards Fermi liquid and its transitions to other phases.