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Register a new userControlled non-Fermi liquids from spacetime dependent couplings
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We construct perturbatively controlled non-Fermi liquids in 3+1 spacetime dimensions, using mild power-law translation breaking interactions. Our mechanism balances the leading tree level effects from such gradients against quantum effects from the interaction between the Fermi surface and a critical boson. We exhibit this in a model where finite density fermions interact with a scalar field via a Yukawa coupling of the form $g(x)propto |x|^kappa$. The approximate non-Fermi liquid behavior arises in the limit of small $kappa$ and persists over an exponentially large window of scales, being cut off by the regime where the coupling becomes large, or by superconducting instabilities. The translation breaking coupling introduces anisotropic deformations of the Fermi surface depending on the direction of the gradient. An extension of this mechanism to 2+1 dimensions could provide a strongly translation-breaking, but weakly coupled non-fermi liquid, something we leave for further work.
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Composite Fermi liquid metals arise at certain special filling fractions in the quantum Hall regime and play an important role as parent states of gapped states with quantized Hall response. They have been successfully described by the Halperin-Lee-Read (HLR) theory of a Fermi surface of composite fermions coupled to a $U(1)$ gauge field with a Chern-Simons term. However, the validity of the HLR description when the microscopic system is restricted to a single Landau has not been clear. Here for the specific case of bosons at filling $ u = 1$, we build on earlier work from the 1990s to formulate a low energy description that takes the form of a {em non-commutative} field theory. This theory has a Fermi surface of composite fermions coupled to a $U(1)$ gauge field with no Chern-Simons term but with the feature that all fields are defined in a non-commutative spacetime. An approximate mapping of the long wavelength, small amplitude gauge fluctuations yields a commutative effective field theory which, remarkably, takes the HLR form but with microscopic parameters correctly determined by the interaction strength. Extensions to some other composite fermi liquids, and to other related states of matter are discussed.
A system with charge conservation and lattice translation symmetry has a well-defined filling $ u$, which is a real number representing the average charge per unit cell. We show that if $ u$ is fractional (i.e. not an integer), this imposes very strong constraints on the low-energy theory of the system and give a framework to understand such constraints in great generality, vastly generalizing the Luttinger and Lieb-Schultz-Mattis theorems. The most powerful constraint comes about if $ u$ is continuously tunable (i.e. the system is charge-compressible), in which case we show that the low-energy theory must have a very large emergent symmetry group -- larger than any compact Lie group. An example is the Fermi surface of a Fermi liquid, where the charge at every point on the Fermi surface is conserved. We expect that in many, if not all, cases, even exotic non-Fermi liquids will have the same emergent symmetry group as a Fermi liquid, even though they could have very different dynamics. We call a system with this property an ersatz Fermi liquid. We show that ersatz Fermi liquids share a number of properties in common with Fermi liquids, including Luttingers theorem (which is thus extended to a large class of non-Fermi liquids) and periodic quantum oscillations in the response to an applied magnetic field. We also establis
We establish the appearance of a qualitatively new type of spin liquid with emergent exceptional points when coupling to the environment. We consider an open system of the Kitaev honeycomb model generically coupled to an external environment. In extended parameter regimes, the Dirac points of the emergent Majorana fermions from the original model are split into exceptional points with Fermi arcs connecting them. In glaring contrast to the original gapless phase of the honeycomb model which requires time-reversal symmetry, this new phase is stable against all perturbations. The system also displays a large sensitivity to boundary conditions resulting from the non-Hermitian skin effect with telltale experimental consequences. Our results point to the emergence of new classes of spin liquids in open systems which might be generically realized due to unavoidable couplings with the environment.
Non-Fermi liquids in $d=2$ spatial dimensions can arise from coupling a Fermi surface to a gapless boson. At finite temperature, however, the perturbative quantum field theory description breaks down due to infrared divergences. These are caused by virtual static bosonic modes, and afflict both fermionic and bosonic correlators. We show how these divergences are resolved by self-consistent boson and fermion self-energies that resum an infinite class of diagrams and correct the standard Eliashberg equations. Extending a previous approach in $d=3-epsilon$ dimensions, we find a new thermal non-Fermi liquid regime that violates the scaling laws of the zero temperature fixed point and dominates over a wide range of scales. We conclude that basic properties of quantum phase transitions and quantum-classical crossovers at finite temperature are modified in crucial ways in systems with soft bosonic fluctuations, and we begin a study of some of the phenomenological consequences.
We consider non-Fermi liquids in which the inelastic scattering rate has an intrinsic particle-hole asymmetry and obeys $omega/T$ scaling. We show that, in contrast to Fermi liquids, this asymmetry influences the low-temperature behaviour of the thermopower even in the presence of impurity scattering. Implications for the unconventional sign and temperature dependence of the thermopower in cuprates in the strange metal (Planckian) regime are emphasized.
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