Presentation on theme: "Pavel Buividovich (Uni Regensburg)"— Presentation transcript:
1Spontaneous chiral symmetry breaking and chiral magnetic effect in Weyl semimetals [1408.4573] Pavel Buividovich(Uni Regensburg)Confinement XI, 8-12 September 2014, St Petersburg
2Weyl semimetals: 3D graphene [Pyrochlore iridate]No mass term for Weyl fermionsWeyl points survive ChSB!!!
3Anomalous (P/T-odd) transport Momentum shift of Weyl points:Anomalous Hall EffectEnergy shift of Weyl points:Chiral Magnetic EffectAlso: Chiral Vortical Effect, Axial Magnetic Effect…Chiral Magnetic Conductivity and Kubo relationsMEMStatic correlators Ground-state transport!!!
4Anomalous transport and interactions Anomalous transport coefficients:Related to axial anomalyDo not receive corrections IFScreening length finite [Jensen,Banerjee,…]Well-defined Fermi-surface [Son, Stephanov…]No Abelian gauge fields [Jensen,Kovtun…]In Weyl semimetals with μA/ induced mass:No screening (massless Weyl fermions/Goldstones)Electric charges interactNon-Fermi-liquid [Buividovich’13]
5Interacting Weyl semimetals Time-reversal breaking WSM:Axion strings [Wang, Zhang’13]RG analysis: Spatially modulatedchiral condensate [Maciejko, Nandkishore’13]Spontaneous Parity Breaking [Sekine, Nomura’13]Parity-breaking WSM: not so clean and not well studied… Only PNJL/σ-model QCD studiesChiral chemical potential μA:Dynamics!!!Circularly polarized laser… But also decays dynamically[Akamatsu,Yamamoto,…][Fukushima, Ruggieri, Gatto’11]
7Simple lattice model Lattice Dirac fermions with contact interactions Lattice Dirac HamiltonianV>0, like charges repelSuzuki-Trotter decompositionHubbard-Stratonovich transformation
8A simple mean-field study Taking everything together…Action of theHubbard fieldPartition functionof free fermions withone-particle hamiltonianHermitianTracelessMean-field approximation:Saddle-point approximation for Φ integrationGaussian fluctuations around saddle pointExact in the limitNontrivial condensation channelsAbsent in PNJL/σ-model studies!!!
9Mean-field approximation: static limit Assuming T→0 andNegative energyof Fermi seaWhat can we add to h(0)to lower the Fermi sea energy?(BUT: Hubbard term suppresses any addition!)Example: Chiral Symmetry BreakingTo-be-Goldstone!
10Mean-field at nonzero μA (cutoff reg.) Possible homogeneouscondensates (assume unbroken Lorentz symmetry)Spectrum at nonzero μA:The effect of μAis similar to mass!!!μA0=0μA0=0.2Anti-screening of μA!!!… but mass lowers the Fermi sea more efficiently
11Crossover vs. Miransky scaling All derivatives are continuous at Vc1/Log(m) goes to zero at VcThis is not the case, we have just crossover
12Linear response and mean-field Externalperturbationchangethe condensate
13Linear response and the mean-field Φx canmimick anylocal termin the Dirac op.Screening ofexternalperturbations
14CME and vector/pseudo-vector “mesons” CME response:Vector meson propagatorMeson mixing with μAρ-mesonPseudovector meson
19Chiral magnetic conductivity vs. V (rescaled by µA)
20Regularizing the problem A lot of interesting questions for numerics…Mean-field level: numerical minimizationMonte-Carlo: first-principle answersConsistent regularization of the problem?Cutoff: no current conservation(and we need <jμjν>…)Lattice: chirality is difficult…BUT: in condmat fermions arenever exactly chiral…Consider Weyl semimetals = Wilson fermions(Complications: Aoki phase etc…)
21Weyl semimetals+μA : no sign problem! One flavor of Wilson-Dirac fermionsInstantaneous interactions (relevant for condmat)Time-reversal invariance: no magnetic interactionsKramers degeneracy in spectrum:Complex conjugate pairsPaired real eigenvaluesExternal magnetic field causes sign problem!Determinant is always positive!!!Chiral chemical potential: still T-invariance!!!Simulations possible with Rational HMC
22Weyl semimetals: no sign problem! Wilson-Dirac with chiral chemical potential:No chiral symmetryNo unique way to introduce μASave as many symmetries as possible [Yamamoto‘10]Counting Zitterbewegung,not worldline wrapping
23Wilson-Dirac: mean-field Rotations/Translations unbroken (???) Im(Eff. Mass) vs VRe(Eff. Mass) vs VμA vs V
24More chiral regularizations? Overlap Hamiltonian for h(0) [Creutz, Horvath, Neuberger]Vacuum energy is still lowered by μA!Local charge densitynot invariant under Lüscher transformationsOnly gauge-type interactions do not breakchiral symmetry explicitly…No sensible mean-field…
25More chiral regularizations? Pauli-Villars regularization?Not strictly chiralNo Hamiltonian formulationOK for chiral anomaly equationOK for CME [Ren’11, Buividovich’13]Regulators also feel μAμA now increases Dirac sea energy!!!(Just an explicit calculation…)
26More chiral regularizations? Overlap fermions with μA? [Buividovich’13]Strictly chiralNo Hamiltonian formulationNo contact-type interactionsOK for chiral anomaly equationOK for CME [Buividovich’13]Again, μA increases vacuum energy!!!Seemingly, TWO interpretations of μADirac sea, finite number of levels (condmat)Infinite Dirac sea with regularization (QFT)What is the physics of these interpretations???
28ConclusionsTwo scenarios for strongly coupled Dirac fermions with chiral imbalance:Condmat-like models with finite Dirac seaChSB enhances chirality imbalanceCME current carried by „vector mesons“Enhancement of CME due to interactionsQFT-like models with regulated Dirac seaChSB suppresses chirality imbalanceRole of regulators not physically clear (so far)New interesting instabilities possible