Hall viscosity and conductivity of two-dimensional chiral  superconductors

Rose, Félix; Golan, Omri; Moroz, Sergej

doi:10.21468/scipostphys.9.1.006

Cited by 9 publications

(7 citation statements)

References 63 publications

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“…o are both real, even functions of ω. In gapped systems η will usually be regular at ω = 0 = q 2 , though exceptions to this rule have recently been found [73].…”

Section: Induced Action and Linear Responsementioning

confidence: 99%

Boundary central charge from bulk odd viscosity: Chiral superfluids

2019

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We derive a low energy effective field theory for chiral superfluids, which accounts for both spontaneous symmetry breaking and fermionic ground-state topology. Using the theory, we show that the odd (or Hall) viscosity tensor, at small wave-vector, contains a dependence on the chiral central charge c of the boundary degrees of freedom, as well as additional non-universal contributions. We identify related bulk observables which allow for a bulk measurement of c. In Galilean invariant superfluids, only the particle current and density responses to strain and electromagnetic fields are required. To complement our results, the effective theory is benchmarked against a perturbative computation within a canonical microscopic model. < l a t e x i t s h a 1 _ b a s e 6 4 = " r L w / X U c T o a 2 Z e K G I 9 H 4 s i a p 2 4 C g = " > A A A B 6 n i c b V B N S w M x E J 2 t X 7 V + V T 1 6 C R b B U 9 k V Q b 0 V v X i s 4 N p C u 5 R s m m 1 D k 2 x I s k J Z + h e 8 e F D x 6 i / y 5 r 8 x 2 + 5 B q w 8 G H u / N M D M v V p w Z 6 / t f X m V l d W 1 9 o 7 p Z 2 9 r e 2 d 2 r 7 x 8 8 m D T T h I Y k 5 a n u x t h Q z i Q N L b O c d p W m W M S c d u L J T e F 3 H q k 2 L J X 3 d q p o J P B I s o Q R b A u p r w w b 1 B t + 0 5 8 D / S V B S R p Q o j 2 o f / a H K c k E l Z Z w b E w v 8 J W N c q w t I 5 z O a v 3 M U I X J B I 9 o z 1 G J B T V R P r 9 1 h k 6 c M k R J q l 1 J i + b q z 4 k c C 2 O m I n a d A t u x W f Y K 8 T + v l 9 n k M s q Z V J m l k i S w M x E J 2 t X 7 V + V T 1 6 C R b B U 9 k V Q b 0 V v X i s 4 N p C u 5 R s m m 1 D k 2 x I s k J Z + h e 8 e F D x 6 i / y 5 r 8 x 2 + 5 B q w 8 G H u / N M D M v V p w Z 6 / t f X m V l d W 1 9 o 7 p Z 2 9 r e 2 d 2 r 7 x 8 8 m D T T h I Y k 5 a n u x t h Q z i Q N L b O c d p W m W M S c d u L J T e F 3 H q k 2 L J X 3 d q p o J P B I s o Q R b A u p r w w b 1 B t + 0 5 8 D / S V B S R p Q o j 2 o f / a H K c k E l Z Z w b E w v 8 J W N c q w t I 5 z O a v 3 M U I X J B I 9 o z 1 G J B T V R P r 9 1 h k 6 c M k R J q l 1 J i + b q z 4 k c C 2 O m I n a d A t u x W f Y K 8 T + v l 9 n k M s q Z V J m l k i S w M x E J 2 t X 7 V + V T 1 6 C R b B U 9 k V Q b 0 V v X i s 4 N p C u 5 R s m m 1 D k 2 x I s k J Z + h e 8 e F D x 6 i / y 5 r 8 x 2 + 5 B q w 8 G H u / N M D M v V p w Z 6 / t f X m V l d W 1 9 o 7 p Z 2 9 r e 2 d 2 r 7 x 8 8 m D T T h I Y k 5 a n u x t h Q z i Q N L b O c d p W m W M S c d u L J T e F 3 H q k 2 L J X 3 d q p o J P B I s o Q R b A u p r w w b 1 B t + 0 5 8 D / S V B S R p Q o j 2 o f / a H K c k E l Z Z w b E w v 8 J W N c q w t I 5 z O a v 3 M U I X J B I 9 o z 1 G J B T V R P r 9 1 h k 6 c M k R J q l 1 J i + b q z 4 k c C 2 O m I n a d A t u x W f Y K 8 T + v l 9 n k M s q Z V J m l k i S w M x E J 2 t X 7 V + V T 1 6 C R b B U 9 k V Q b 0 V v X i s 4 N p C u 5 R s m m 1 D k 2 x I s k J Z + h e 8 e F D x 6 i / y 5 r 8 x 2 + 5 B q w 8 G H u / N M D M v V p w Z 6 / t f X m V l d W 1 9 o 7 p Z 2 9 r e 2 d 2 r 7 x 8 8 m D T T h I Y k 5 a n u x t h Q z i Q N L b O c d p W m W M S c d u L J T e F 3 H q k 2 L J X 3 d q p o J P B I ...

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“…o are both real, even functions of ω. In gapped systems η will usually be regular at ω = 0 = q 2 , though exceptions to this rule have recently been found [73].…”

Section: Induced Action and Linear Responsementioning

confidence: 99%

Boundary central charge from bulk odd viscosity: Chiral superfluids

2019

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“…3is valid if this symmetry breaking is explicit, i.e., H does not commute with P and T separately. Here we consider the case where H is P, Tsymmetric, but these are broken down to PT spontaneously, as in, e.g., intrinsic topological superfluids and superconductors [61,99,100]. We first generalize Eq.…”

Section: Spontaneous Chiralitymentioning

confidence: 99%

Intrinsic sign problem in fermionic and bosonic chiral topological matter

Golan

Smith

Ringel

2020

Phys. Rev. Research

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The infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative, allowing efficient simulations on classical computers. Motivated by long-standing open problems in many-body physics, as well as fundamental questions in quantum complexity, the possibility of intrinsic sign problems, where a phase of matter admits no sign-problem-free representative, was recently raised but remains largely unexplored. Here we establish the existence of an intrinsic sign problem in a broad class of gapped, chiral, topological phases of matter. Within this class, we exclude the possibility of stoquastic Hamiltonians for bosons (or "qudits") and of sign-problem-free determinantal Monte Carlo algorithms for fermions. The intrinsically sign-problematic class of phases we identify is defined in terms of topological invariants with clear observable signatures: the chiral central charge and the topological spins of anyons. We obtain analogous results for phases that are spontaneously chiral, and present evidence for an extension of our results that applies to both chiral and nonchiral topological matter.

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“…(9.81) of the book [1], six Hall viscosity terms in 3 He-A with coefficients ⟂ , ∥ and R a with a = 1, 2, 3, 4 are presented. The Hall viscosity in the 2D chiral superfluids is now under discussion in the literature, see review [46]. The quantization of the Hall viscosity in terms of the orbital momentum is suggested.…”

Section: Chiral Anomaly Angular Momentum Paradoxmentioning

confidence: 99%