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Springer

Received: May 25, 2020 Accepted: June 18, 2020 Published: July 8, 2020

Vladimir Juriˇ ci´ c,a Ignacio Salazar Landeab and Rodrigo Soto-Garridoc a

Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden b Instituto de F´ısica de La Plata — CONICET, C.C. 67, 1900 La Plata, Argentina c Facultad de F´ısica, Pontificia Universidad Cat´ olica de Chile, Vicu˜ na Mackenna 4860, Santiago, Chile

E-mail: [email protected], [email protected], [email protected] Abstract: Topological phases of matter have recently attracted a rather notable attention in the community dealing with the holographic methods applied to strongly interacting condensed matter systems. In particular, holographic models for gapless Weyl and multiWeyl semimetals, characterized on a lattice by the monopole-antimonopole defects of the Berry curvature in momentum space, were recently formulated. In this paper, motivated by the quest for finding topological holographic phases, we show that holographic model for multi-Weyl semimetals features a rather rich landscape of phases. In particular, it includes a novel phase which we dub xy nematic condensate, stable at strong coupling, as we explicitly show by the free energy and the quasi-normal mode analyses. Furthermore, we provide its characterization through the anomalous transport coefficients. We hope that our findings will motivate future works exploring the holographic realizations of the topological phases. Keywords: AdS-CFT Correspondence, Anomalies in Field and String Theories, Black Holes, Holography and condensed matter physics (AdS/CMT) ArXiv ePrint: 2005.10387

c The Authors. Open Access, Article funded by SCOAP3 .

https://doi.org/10.1007/JHEP07(2020)052

JHEP07(2020)052

Phase transitions in a holographic multi-Weyl semimetal

Contents 1

2 Multi Weyl semimetals

3

3 The holographic model

4

4 The phase transitions 4.1 The nematic phase 4.2 The xy nematic condensate

5 5 6

5 Linear stability 5.1 The Higgs sector 5.2 The Goldstone sector

8 9 9

6 Anomaly induced transport

10

7 Discussion and future directions

13

1

Introduction

The paradigm of topological states of matter is by now well established, where in contrast to the usual Landau’s symmetry classification, the characterization of a phase is provided in terms of the topological invariants [1, 2]. The prime examples of fermionic gapped topological phases are the integer quantum Hall states [3], with the time-reversal symmetry broken, for instance, by a magnetic field. As such, they are characterized in terms of the Chern number of the occupied electronic bands [4], directly related to the quantized Hall conductance in these systems. As a consequence of the nontrivial electronic topology, these topological states feature topologically protected gapless chiral edge modes, providing an example of the generic property of a topological state of matter: the (condensed-matter) bulk-boundary correspondence. The notion of topological phases is also operative when tim