Perturbative non-Fermi liquids from dimensional regularization

Dalidovich, Denis; Lee, Sung-Sik

doi:10.1103/physrevb.88.245106

Cited by 137 publications

(209 citation statements)

References 67 publications

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“…This is again due to the commuting CDW vertices in contrast to the anti-commuting SDW vertices in Eq. (36). Therefore the two-loop diagram further reduces c for the CDW case, while it stops c from flowing to zero for the SDW case.…”

Section: Charge Density Wave Criticalitymentioning

confidence: 92%

“…Consequently, the size of the Fermi surface enters in the low-energy scaling of physical quantities which are insensitive to the size of Fermi surface in the original two-dimensional theory. An alternative strategy is to reduce the density of states of the collective mode [33,34], or the fermions [35][36][37]. This is achieved either by modifying the dispersion, or embedding the one-dimensional Fermi surface in a higher dimensional space.…”

Section: Introductionmentioning

confidence: 99%

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Anisotropic non-Fermi liquids

Sur

Lee

2016

Phys. Rev. B

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We study non-Fermi liquid states that arise at the quantum critical points associated with the spin density wave (SDW) and charge density wave (CDW) transitions in metals with twofold rotational symmetry. We use the dimensional regularization scheme, where a one-dimensional Fermi surface is embedded in 3 − ǫ dimensional momentum space. In three dimensions, quasilocal marginal Fermi liquids arise both at the SDW and CDW critical points : the speed of the collective mode along the ordering wavevector is logarithmically renormalized to zero compared to that of Fermi velocity. Below three dimensions, however, the SDW and CDW critical points exhibit drastically different behaviors. At the SDW critical point, a stable anisotropic non-Fermi liquid state is realized for small ǫ, where not only time but also different spatial coordinates develop distinct anomalous dimensions. The non-Fermi liquid exhibits an emergent algebraic nesting as the patches of Fermi surface are deformed into a universal power-law shape near the hot spots. Due to the anisotropic scaling, the energy of incoherent spin fluctuations disperse with different power laws in different momentum directions. At the CDW critical point, on the other hand, the perturbative expansion breaks down immediately below three dimensions as the interaction renormalizes the speed of charge fluctuations to zero within a finite renormalization group scale through a two-loop effect. The difference originates from the fact that the vertex correction anti-screens the coupling at the SDW critical point whereas it screens at the CDW critical point.

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Section: Charge Density Wave Criticalitymentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Anisotropic non-Fermi liquids

Sur

Lee

2016

Phys. Rev. B

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“…[13][14][15][16][17] A different example which does not suffer from these complications 16,18 (see, however, footnote 19) is the transition associated with the onset of Ising-nematic order, characterized by spontaneous breaking of a four-fold rotational symmetry of the lattice to a two-fold subgroup. 18,[20][21][22][23][24][25][26][27][28][29][31][32][33][34][35][36] The order parameter in this case is just a real Ising field φ(x). Growing evidence for such order has been found in a number of physical systems including cuprate, 37-43 pnictide…”

Section: -3mentioning

confidence: 99%

Cooper pairing in non-Fermi liquids

et al. 2015

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States of matter with a sharp Fermi-surface but no well-defined Landau quasiparticles arise in a number of physical systems. Examples include: (i) quantum critical points associated with the onset of order in metals; (ii) spinon Fermi-surface (U(1) spin-liquid) state of a Mott insulator; (iii) Halperin-Lee-Read composite fermion charge liquid state of a half-filled Landau level. In this work, we use renormalization group techniques to investigate possible instabilities of such non-Fermiliquids in two spatial dimensions to Cooper pairing. We consider the Ising-nematic quantum critical point as an example of an ordering phase transition in a metal, and demonstrate that the attractive interaction mediated by the order parameter fluctuations always leads to a superconducting instability. Moreover, in the regime where our calculation is controlled, superconductivity preempts the destruction of electronic quasiparticles. On the other hand, the spinon Fermi-surface and the Halperin-Lee-Read states are stable against Cooper pairing for a sufficiently weak attractive shortrange interaction; however, once the strength of attraction exceeds a critical value, pairing sets in. We describe the ensuing quantum phase transition between (i) U (1) and Z2 spin-liquid states; (ii) Halperin-Lee-Read and Moore-Read states.

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“…Strong correlation and quantum critical fluctuation often make it challenging to study the non-fermi liquids through the standard diagrammatic approach, and various expansion methods have been developed for that purpose [4][5][6][7][8] . Fortunately, there exist some exactly soluble models for non-Fermi liquid states which do not rely on perturbation theory.…”

Section: Introductionmentioning

confidence: 99%

Instability of the non-Fermi-liquid state of the Sachdev-Ye-Kitaev model

Bi¹,

Jian²,

You³

et al. 2017

Phys. Rev. B

104

120

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We study a series of perturbations on the Sachdev-Ye-Kitaev (SYK) model. We show that the maximal chaotic non-Fermi liquid phase described by the ordinary q = 4 SYK model has marginally relevant/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. Starting with the SYKq model with a q−fermion interaction, similar perturbations can lead to a series of new fixed points with continuously varying exponents.

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Perturbative non-Fermi liquids from dimensional regularization

Cited by 137 publications

References 67 publications

Anisotropic non-Fermi liquids

Anisotropic non-Fermi liquids

Cooper pairing in non-Fermi liquids

Instability of the non-Fermi-liquid state of the Sachdev-Ye-Kitaev model

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