Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session V45: Beyond Fermi Liquids I |
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Sponsoring Units: DCMP Chair: Erez Berg, Univ of Chicago Room: LACC 505 |
Thursday, March 8, 2018 2:30PM - 2:42PM |
V45.00001: Local criticality and marginal Fermi liquid behavior in a translationally invariant solvable model I : Thermodynamics and single particle properties Debanjan Chowdhury, Yochai Werman, Erez Berg, Senthil Todadri An ubiquitous feature across many strongly-correlated materials is the appearance of a metallic phase without well defined quasiparticle excitations and non-Fermi liquid properties. The non-Fermi liquid properties often persist over a broad range of temperatures above a small crossover scale, below which conventional Fermi liquid behavior is recovered. In this work, we construct examples of translationally invariant models of strongly-correlated metals with on-site, multi-orbital interactions of the Sachdev-Ye-Kitaev form. When the number of orbitals is taken to be large, we observe interesting crossovers as a function of increasing temperature from a renormalized Fermi liquid with a sharp Fermi surface to a non-Fermi liquid regime with local quantum criticality and no sign of a Fermi-surface. By extending the model to have multiple bands with different bandwidths, we also construct examples of marginal and non-Fermi liquid metals with a critical Fermi surface and singular self-energy. We discuss the thermodynamic properties and compute the single-particle spectral functions in the different regimes. |
Thursday, March 8, 2018 2:42PM - 2:54PM |
V45.00002: Local criticality and marginal Fermi liquid behavior in a translationally invariant solvable model II : Transport and beyond Erez Berg, Debanjan Chowdhury, Yochai Werman, Senthil Todadri One of the hallmarks of bad metal behavior in many strongly-correlated materials is the existence of a broad range of temperatures, upto a low crossover scale, over which the resistivity shows striking deviation from Fermi liquid behavior without any apparent sign of saturation. In this work, we consider the transport properties of a large class of translationally invariant models of strongly-correlated metals with on-site, multi-orbital interactions of the Sachdev-Ye-Kitaev form in the limit when the number of orbitals is taken to be large. In a generalized version of the model with multiple bands, we discuss the transport properties of the marginal and non-Fermi liquid metals and find no evidence of a `Planckian-bound' on the transport scattering rates. We also draw connections to many-body quantum chaos. |
Thursday, March 8, 2018 2:54PM - 3:06PM |
V45.00003: Instability of the non-Fermi liquid state of the Sachdev-Ye-Kitaev Model Zhen Bi, Chao-Ming Jian, Yizhuang You, Kelly Pawlak, Cenke Xu The Sachdev-Ye-Kitaev (SYK) model is an intriguing 0+1d strongly interacting disordered model of non-Fermi liquid states with exact solution and possible holographic duality. In this talk, I will consider a series of perturbations on the SYK model. We show that the maximal chaotic non-Fermi-liquid phase described by the ordinary SYK model has marginally relevant or irrelevant (depending on the sign of the coupling constants) four-fermion perturbations allowed by symmetry. Changing the sign of one of these four-fermion perturbations leads to a continuous chaotic-nonchaotic quantum phase transition of the system accompanied by a spontaneous time-reversal symmetry breaking. We also studied a generalized 0+1d interacting disordered fermion model which has a series of new fixed points with continuously varying exponents. |
Thursday, March 8, 2018 3:06PM - 3:18PM |
V45.00004: Higher-dimensional SYK Non-Fermi Liquids at Lifshitz transitions Sumilan Banerjee, Arijit Haldar, Vijay Shenoy We address the key open problem of a higher-dimensional generalization of the Sachdev-Ye-Kitaev |
Thursday, March 8, 2018 3:18PM - 3:30PM |
V45.00005: Quantum-Classical Correspondence and chaotic mobility edge for Fast Scramblers Ehud Altman, Thomas Scaffidi We introduce a semiclassical version of the Sachdev-Ye-Kitaev model for which chaos can be understood as arising from diverging geodesics on a SO(N) manifold equipped with a random metric with locally negative curvature. The global Lyapunov exponent of the classical model is found to grow linearly with temperature, with a slope that can exceed the quantum bound. The bound on chaos is understood as a reversed ``chaotic mobility edge'' in the classical Lyapunov spectrum, separating the lower part of the spectrum for which a classical chaos picture is valid from the higher part of the spectrum for which quantum interference effects are strong enough to destroy chaos. The mobility edge corresponds to a curvature radius of the order of the de Broglie wavelength. |
Thursday, March 8, 2018 3:30PM - 3:42PM |
V45.00006: Numerics of Fast Scrambling in the SYK Model Bryce Kobrin, Christopher Olund, Douglas Stanford, Joel Moore, Norman Yao Out-of-time-order correlators (OTOCs) offer a useful tool for characterizing the approach to chaos in strongly coupled quantum systems. However, exact diagonalization numerics of OTOCs are limited to small system sizes and controlled finite size extrapolation techniques are few. To this end, we utilize massively parallel Krylov methods to calculate OTOCs in the Sachdev-Ye-Kitaev (SYK) model for more than 50 Majorana fermions. For small systems, we show that, consistent with prior results, the Lyapunov exponent exhibits a temperature dependence opposite to that of the analytic expectation. However, for large enough systems, we find that this behavior flips and the correct qualitative trend emerges. More quantitatively, we develop a finite-size rescaling procedure for extracting Lyapunov exponents and compare our results to exact calculations in the thermodynamic limit. We observe excellent agreement at high temperatures and systematic improvements in the low-temperature behavior as we scale to larger system sizes. |
Thursday, March 8, 2018 3:42PM - 3:54PM |
V45.00007: Lowest Landau Level Theory of Composite Fermi Liquid for SU(2) boson at total filling 1 Ya-Hui Zhang, T. Senthil We microscopically derived an effective field theory for composite fermi liquid(CFL) in lowest landau level for SU(2) boson at total filling 1 by generalizing N.Read's initial approach for spinless boson. In our theory,the Girvin-MacDonald-Platzman (GMP) algebra is satisfied exactly to all orders. At low energy(close to fermi surface), the effective field theory has two fermi surfaces coupled to one emergent U(1) gauge field without self chern simons term. In addition, each fermi surface has a Pi berry phase. As a result, the low energy theory can be UV completed to QED3 with two dirac fermions. Similar to Son's dirac theory for fermionic half-filled landau level CFL, physical density here is also carried by emergent flux. |
Thursday, March 8, 2018 3:54PM - 4:06PM |
V45.00008: Quantum Chaos in an Electron-Phonon Bad Metal Yochai Werman, Steven Kivelson, Erez Berg We calculate the scrambling rate and the butterfly velocity associated with the growth of quantum chaos for a solvable large-N electron-phonon system. We study a temperature regime in which the electrical resistivity of this system exceeds the Mott-Ioffe-Regel limit and increases linearly with temperature - a sign that there are no long-lived charged quasiparticles - although the phonons remain well-defined quasiparticles. The long-lived phonons determine the scrambling rate, rendering it parametrically smaller than the theoretical upper-bound. Significantly, the chaos properties seem to be intrinsic - and are the same for electronic and phononic operators. We consider both dispersive and non-dispersive phonons. In either case, we find that the scrmabling rate is proportional to the inverse phonon lifetime, and the butterfly velocity is proportional to the effective phonon velocity. The thermal and chaos diffusion constants are always comparable, while the charge diffusion constant may be either larger or smaller than the chaos diffusion constant. |
Thursday, March 8, 2018 4:06PM - 4:18PM |
V45.00009: Sequential Kondo destruction in an SU(4) Bose-Fermi Kondo model Rong Yu, Ang Cai, Emilian Nica, Chia-Chuan Liu, Silke Buehler-Paschen, Qimiao Si Quantum criticality and the beyond-Landau physics of Kondo destruction [1,2] in heavy fermion systems with multipolar degrees of freedom is attracting considerable interest. Recent experiment on the heavy fermion compound Ce3Pd20Si6 shows evidence of two consecutive Fermi surface collapsing quantum phase transitions (QPT) as a function of magnetic field [3]. We advance a theory of two stages of Kondo effect. We consider an SU(4) Bose-Fermi Kondo model with both spin and orbital degrees of freedom, which represents an effective model for a multipolar Kondo lattice system. As a function of coupling strength to the bosonic baths, we find that a generic trajectory in the parameter space contains two QPTs, each being associated with the Kondo destruction of spin or orbital degrees of freedom. For Kondo lattice, this corresponds to two stages of Fermi surface jump, thus providing a natural understanding of the experimental findings. |
Thursday, March 8, 2018 4:18PM - 4:30PM |
V45.00010: Luttinger Liquid Instabilities in n-component 1-D Lattice Fermionic Systems Yuchi He, Binbin Tian, Roger Mong, David Pekker We investigate phases and phase transitions of n-component 1-D lattice fermions models by DMRG and bosonization method. We consider models which are the deformation of SU(n) Hubbard model. For example, masses and interactions can be anisotropic. We examine the instabilities (phases) by studying which modes are gapped and what composite operators remain gapless. SU(n) Hubbard models have "spin" gapped phases and charge gapped/fully gapped phases. We find that the above phases are all robust under moderate deformation. For sufficiently large deformation, we explore the possible new phases such as p-wave pairs or "p-wave" trions. |
Thursday, March 8, 2018 4:30PM - 4:42PM |
V45.00011: Quantum Entanglement of the Sachdev-Ye-Kitaev Models Chunxiao Liu, Xiao Chen, Leon Balents The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical model of fermions interacting with $q$-body random couplings. For $q=2$, it describes free particles, and is non-chaotic in the many-body sense, while for $q>2$ it is strongly interacting and exhibits many-body chaos. In this work we study the entanglement entropy (EE) of the SYK$q$ models, for a bipartition of $N$ real or complex fermions into subsystems containing $2m$ real/$m$ complex fermions and $N-2m$/$N-m$ fermions in the remainder. For the free model SYK2, we obtain an analytic expression for the EE, derived from the $\beta$-Jacobi random matrix ensemble. Furthermore, we use the replica trick and path integral formalism to show that the EE is maximal for when one subsystem is small, i.e. $m\ll N$, for arbitrary $q$. We also demonstrate that the EE for the SYK4 model is noticeably smaller than the Page value when the two subsystems are comparable in size, i.e. $m/N$ is $O(1)$. Finally, we explore the EE for a model with both SYK2 and SYK4 interaction and find a crossover from SYK2 (low temperature) to SYK4 (high temperature) behavior as we vary energy. |
Thursday, March 8, 2018 4:42PM - 4:54PM |
V45.00012: Sachdev-Ye-Kitaev models with complex fermions Wenbo Fu, Yingfei Gu, Subir Sachdev We studied Sachdev-Ye-Kitaev models with complex fermions. We diagonalized the kernel matrix at finite chemical potential, and found the reparameterization and phase modes in the conformal limit. From the kernel, we read off the spectrum of operators that appear in the OPE expansion of two fermions. And from the UV correction in the two point function, we analyzed the kernel correction that leads to the effective action, and relates to the chaos behavior. |
Thursday, March 8, 2018 4:54PM - 5:06PM |
V45.00013: Strange-Half Metals and Mott Insulators in SYK Models Arijit Haldar, Vijay Shenoy We study a dual-flavor fermion model where each of the flavors form a Sachdev-Ye-Kitaev(SYK) system with arbitrary q-body interactions. The crucial new element is an all-to-all r-body interaction between the two flavors. At high temperatures the model shows a strange metal phase where both flavors are gapless, similar to the usual single-flavor SYK model. Upon reducing temperature, the coupled system undergoes transitions to previously unseen phases in the SYK framework -- first, a strange-half metal phase where one flavor remains a strange metal while the other is gapped, and second, an insulating phase of the Mott kind where both flavors are gapped. At a fixed low temperature we obtain transitions between these phases by tuning the relative fraction of sites for each flavor. We discuss the physics of these phases and the nature of transitions between them. This work provides an example of an instability of the strange metal with potential to provide new routes to study strongly correlated systems through the rich physics contained in SYK like models. arXiv:1703.05111v1 |
Thursday, March 8, 2018 5:06PM - 5:18PM |
V45.00014: Generalized SYK models: non-Fermi Liquid and quantum chaos Pengfei Zhang, Hui Zhai, Ruihua Fan, Yiming Chen, Xin Chen The Sachdev-Ye-Kitaev (SYK) model is a concrete solvable model to study non-Fermi liquid properties and quantum chaos. I will discuss two generalizations of the SYK model that contains two SYK models with different number of Majorana modes. In the first model, they are coupled by quadratic terms and the solution shows a quantum phase transition between two non-Fermi liquid chaotic phases. In the second model, they are coupled by random interaction and we find the chaotic behavior could be tuned. |
Thursday, March 8, 2018 5:18PM - 5:30PM |
V45.00015: The Conditions for $l=1$ Pomeranchuk Instability in a Fermi Liquid Yi-Ming Wu, Avraham Klein, Dmitrii Maslov, Andrey Chubukov We analyze the forms of static spin and charge susceptibilities in $l >0$ channels in a Galilean-invariant Fermi liquid, to verify recent claim that $l=1$ Pomeranchuk instability in a Fermi liquid is absent. We first show that, because a charge or a spin order parameter with $l>0$ is, in general not a conserved quantity, the corresponding susceptibility, $\chi_l$, has contributions from states near and away from the Fermi surface. We discuss a generic form of $\chi_l$ and show the results for $l=1$ and $l=2$ to second order in the Hubbard $U$. For $l=1$, we show that $\chi_1$ changes qualitatively between the special case when the order parameter coincides with the current (the form-factor is $A {\bf k}$), and a generic case when the form-factor is ${\bf k} f(|k|)$ and $f(|k|)$ is not a constant. In the first case, the corrections to free-fermion result for $\chi_{l=1}$ disappear, even in the spin case, and $p-$wave Pomeranchuk instability does not occur. In perturbative calculations, this comes about due to a particular cancellation between contributions to $\chi_1$ from states near and away from the Fermi surface. In a generic case, we found that such cancellation does not occur and p-wave spin Pomeranchuk instability develops for strong enough interaction. |
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