Non-Fermi-liquid behavior and anomalous suppression of Landau damping in layered metals close to ferromagnetism

We analyse the low-energy physics of nearly ferromagnetic metals in two spatial dimensions using the functional renormalization group technique. We find a new low-energy fixed point, at which the fermionic (electron-like) excitations are non-Fermi-liquid ($z_f = 13/10$) and the magnetic fluctuations exhibit an anomalous Landau damping whose rate vanishes as $\Gamma_{\bf q} \sim \vert {\bf q} \vert^{3/5}$ in the low-$\vert {\bf q} \vert$ limit. We discuss this renormalization of the Landau-damping exponent, which is the major novel prediction of our work, and highlight the possible link between that renormalization and neutron-scattering data on UGe$_2$ and related compounds. Implications of our analysis for YFe$_2$Al$_{10}$ are also discussed.Comment: 5 pages, 3 figures; action modified to include spin of fermions, resulting in quantitative changes to exponents but same essential physic

Infinite-redshift localized states of Dirac fermions under Einsteinian gravity

We present a set of localized states for an even number of Dirac fermions under Einsteinian gravity that have an infinite central redshift. Near the center of the localized state the components of the Dirac spinor and the spacetime metric all show simple power-law dependences on the radial distance; further out the fermionic wave function decays to zero and the spacetime becomes asymptotically flat. We show that this "central"solution of the equations of motion can be used to understand much of the structure observed by Finster, Smoller, and Yau [Phys. Rev. D 59, 104020 (1999)] in their numerical solutions of the same problem at finite central redshift.Publisher PDFPeer reviewe

Non-Fermi liquid fixed points and anomalous Landau damping in a quantum critical metal

Funding: CM-CDT under UK Engineering and Physical Sciences Research Council (EPSRC) (UK) Grant No. EP/L015110/1 (M.J.T.); TOPNES programme under EPSRC (UK) Grant No. EP/I031014/1 (C.A.H.).We present a functional renormalization-group calculation of the properties of a quantum critical metal in d=2 spatial dimensions. Our theory describes a general class of Pomeranchuk instabilities with Nb flavors of boson. At small Nb we find a family of fixed points characterized by weakly non-Fermi-liquid behavior of the conduction electrons and z≈2 critical dynamics for the order-parameter fluctuations, in agreement with the scaling observed by Schattner et al. [Phys. Rev. X 6, 031028 (2016)] for the Ising-nematic transition. Contrary to recent suggestions that this represents an intermediate regime en route to the scaling limit, our calculation suggests that this behavior may persist all the way to the critical point. As the number of bosons Nb is increased, the model's fixed-point properties cross over to z≈1 scaling and non-Fermi-liquid behavior similar to that obtained by Fitzpatrick et al. [Phys. Rev. B 88, 125116 (2013)].Publisher PDFPeer reviewe

Nonlinear effects in the excited states of many-fermion Einstein-Dirac solitons

Funding: P. E. D. L. acknowledges funding from a St Leonards scholarship from the University of St Andrews and from UKRI under EPSRC Grant No. EP/R513337/1.We present an analysis of excited-state solutions for a gravitationally localized system consisting of a filled shell of high-angular-momentum fermions, using the Einstein-Dirac formalism introduced by Finster, Smoller, and Yau [Phys. Rev. D 59, 104020 (1999)]. We show that, even when the particle number is relatively low (Nf ≥ 6), the increased nonlinearity in the system causes a significant deviation in behavior from the two-fermion case. Excited-state solutions can no longer be uniquely identified by the value of their central redshift, with this multiplicity producing distortions in the characteristic spiraling forms of the mass-radius relations. We discuss the connection between this effect and the internal structure of solutions in the relativistic regime.Publisher PDFPeer reviewe

Fermion self-trapping in the optical geometry of Einstein-Dirac solitons

Funding: St Leonards scholarship from the University of St Andrews and from UKRI under EPSRC Grant No. EP/R513337/1 (P.E.D.L).We analyze gravitationally localized states of multiple fermions with high angular momenta, in the formalism introduced by Finster, Smoller, and Yau [Phys Rev. D 59, 104020 (1999)]. We show that the resulting solitonlike wave functions can be naturally interpreted in terms of a form of self-trapping, where the fermions become localized on shells the locations of which correspond to those of “bulges” in the optical geometry created by their own energy density.Publisher PDFPeer reviewe

Spin-models, dynamics and criticality with atoms in tilted optical superlattices

Funding: Strathclyde: UK EPSRC Programme Grant DesOEQ (EP/P009565/1), the European Union Horizon 2020 collaborative project QuProCS — QuantumProbes for Complex Systems (Grant Agreement No. 641277), and by the EOARD via AFOSR Grant No. FA9550-18-1-0064.We show that atoms in tilted optical superlattices provide a platform for exploring coupled spin chains of forms that are not present in other systems. In particular, using a period-2 superlattice in one dimension, we show that coupled Ising spin chains with XZ and ZZ spin coupling terms can be engineered. We use optimized tensor network techniques to explore the criticality and nonequilibrium dynamics in these models, finding a tricritical Ising point in regimes that are accessible in current experiments. These setups are ideal for studying low-entropy physics, as initial entropy is “frozen-out” in realizing the spin models, and provide an example of the complex critical behavior that can arise from interaction-projected models.Publisher PDFPeer reviewe

Resonant two-site tunnelling dynamics of bosons in a tilted optical superlattice

Funding: Strathclyde: UK EPSRC Program Grant DesOEQ (No.EP/P009565/1), the European Union Horizon 2020 collaborative project Quantum Probes for Complex Systems (Grant Agreement No. 641277), and by the EOARD via AFOSR Grant No. FA9550-18-1-0064.We study the nonequilibrium dynamics of a one-dimensional Bose-Hubbard model in a gradient potential and a superlattice, beginning from a deep Mott insulator regime with an average filling of one particle per site. Studying a quench that is near resonance to tunneling of the particles over two lattice sites, we show how a spin model emerges consisting of two coupled Ising chains that are coupled by interaction terms in a staggered geometry. We compare and contrast the behavior in this case with that in a previously studied case where the resonant tunneling was over a single site. Using optimized tensor network techniques to calculate finite-temperature behavior of the model, as well as finite-size scaling for the ground state, we conclude that the universality class of the phase transition for the coupled chains is that of a tricritical Ising point. We also investigate the out-of-equilibrium dynamics after the quench in the vicinity of the resonance and compare dynamics with recent experiments realized without the superlattice geometry. This model is directly realizable in current experiments and reflects a general way to realize spin models with ultracold atoms in optical lattices.Publisher PDFPeer reviewe