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Topological Matter and Crystal Symmetry: From Microscopic Structure to Phenomenology

Periodic Reporting for period 1 - TMCS (Topological Matter and Crystal Symmetry: From Microscopic Structure to Phenomenology)

Reporting period: 2019-01-01 to 2020-06-30

"This project is devoted to developing an understanding of Topological States of Matter, using Crystalline Symmetry as an organizing principle. These unconventional quantum many-particle states are captured by subtle structures in the quantum entanglement between different degrees of freedom. While some can be understood from a weakly-interacting starting point, many interesting topological phases involve strong interactions. New tools are required to analyse their properties.

Such states could form a platform for quantum computing devices that are naturally protected from external sources of ""noise"": topological information is non-locally encoded and hence more robust. Many topological systems have unconventional electromagnetic and optical properties, that could have hitherto-unsuspected applications. They are a source of intrinsic interest to scientists, as the techniques used to study them have deep links to fundamental questions in particle and statistical physics, beyond their direct relevance to applications.

We will develop tools to identify, simulate and experimentally detect these phases. Analytical projects will explore classification schemes for topological phases, new ""fracton"" topological orders, and realizations in solid-state systems. Numerical projects will develop new simulation techniques for these phases. Experimental subprojects will identify new probes of topological systems."
"""Fracton"" models: We have clarified the role of translational symmetries in these models (Subproject 1d) and used it to find proximate broken symmetries. On the numerical side (2c), with Dr. S. Gazit and others we performed a warm-up analysis of interacting random gauge theories in 2D (before delving directly into fracton simulations). The numerical algorithms are not specific to random systems. The study of these gauge theories (with both disorder and without)is now included in subproject 2c. [The ERC panel suggested also stuudying disordered systems.]

Phenomenology of semimetals (3a): we performed quantum oscillation studies of a topological nodal line semimetal with Dr. A. Coldea’s group.

Spectroscopy of topological matter (3b): With A. Yazdani’s group we developed a of domain walls in quantum Hall nematics. We discovered a hidden non-symmorphic symmetry that explains experiments on the quantum critical magnet CoNb2O6, with R. Coldea’s group.

New developments:
Moiré systems. These unusual 2D materials are deeply linked to the ideas on quantum Hall nematic states and to spin liquid and fractionalization ideas (1a,1b, 3b). We already have 1 publication and 3 preprints. We have developed an advanced code for such systems, folded into 2a.

“Higher order"" topological phases. These phases, whose existence relies on crystal symmetry, fits naturally into the general understanding of topological phases of matter (1a-b). We have 1 publication in Physical Review Letters, and are completing classification of ""surface topological order"" of these states. These will help us understand the interplay of interactions, symmetry and topology. An ETH student working on this will join the project for a PhD in 2020.

Quasicrystalline Dimer models. These have links to fractal structures such as fractons, moiré physics, and frustrated magnets. Our first paper has appeared in Physical Review X. At the classical level already these display many similarities with spin models used to study quantum magnets and gapless spin liquids (1c), fracton phases (1d, 2c), and so work on this direction has been included into these sub-projects. The issue of quasiperiodicity is also linked naturally to ""moire"" physics.

SYK Model. Given the challenge of numerics on heavy fermion systems and frustrated magnets we have used the ""Sachdev-Ye-Kitaev"" model to explore such issues in reduced dimensions. SYK (i) is a toy model for a 0D non-Fermi liquid (ii) has ""scrambling"" properties linked to difficulty of simulating dynamics efficiently; and (iii) has extensive degeneracy in the thermodynamic limit, as in frustrated magnets. The PI and Dr. Biswas have been exploring the SYK model with numerical and analytical ideas.


Nonlinear spectroscopy. This has been identified as a potentially revolutionary probe of correlated topological systems, where Crystalline symmetry is an important aspect This work complements other research activity in the PI's group on random systems, since the numerical and analytical approaches to novel spectroscopy in the random and topological settings have common features but the resulting responses can be distinguished (unlike in linear response.) Understanding nonlinear response has now been included into 3a,b. Early work has led to a preprint under review in Physical Review Letters, and the PI and Dr. Biswas are working with students to understand the nonlinear response of confined fractionalized excitations.

Some projects met obstacles. Numerics on correlated phases have run into roadblocks; however the appointment of new PDRAs (arriving Nov 2020) will help advance this project. Also, there was early hope in classical Monte-Carlo simulations of fracton-like models (2c); however, an analysis of models with corner-sharing triangles (proposed as one route to ""classical"" fracton physics) yielded a negative result. This may still be interesting as there is a chance this result points at a fundamental obstruction of this approach."
Progress beyond state of the art is reported in the following articles and preprints:
1. Quantum hall nematic domain walls [K. Agarwal, M.T. Randeria, A. Yazdani, S.L. Sondhi, and SAP, Phys. Rev. B 100, 165103 (2019).]
2. Quasicrystallline dimer models [F. Flicker, S.H. Simon, and SAP, Phys. Rev. X 10, 011005 (2020).]
3. Surface Topological Order for Higher Order Topological Phases [A. Tiwari, M.-H. Li, B.A. Bernevig, T. Neupert, and SAP, Phys. Rev. Lett. 124, 046801 (2020).]
4. Quantum oscillations in nodal-line semimetals [Y.H. Kwan, P. Reiss, Y. Han, M. Bristow, D. Prabhakaran, D. Graf, A. McCollam, SAP, and A.I. Coldea, Phys. Rev. Research 2, 012055(R) (2020).]
5. Parallel magnetic field in twisted bilayer graphene [Y. H. Kwan, SAP, and S. L. Sondhi, Phys. Rev. B 101, 205116 (2020).]
6. Exciton physics in moire systems [Y.H. Kwan, Y. Hu, S.H. Simon, and SAP, arXiv:2003.11560 (2020), arXiv:2003.11559 (2020)]
8. Nonsymmorphic symmetries in 1d magnets [M. Fava, R. Coldea, and SAP, arXiv:2004.04169 (2020), to appear, PNAS]
9. Crystal-Symmetry-enriched fractons [M. Pretko, SP, M. Hermele, arXiv:2004.14393 (2020)]
10. Nonlinear response of random magnets, [SAP and S. Gopalakrishnan, arXiv:2007.04323 (2020).
11. Numerics for inhomogeneous moire systems, [Y.H. Kwan, G. Wagner, N. Chakraborty, S.H. Simon, SAP, arXiv:2007.07903 (2020)]

Expected Future Results:
1. Surface topological order for crystal-symmetry-protected topological phases.
2. Links between the SYK models and frustrated magnetic systems
3. Analytical results on exciton band topology, many-body exciton physics in Moire systems
4. Theories of moiré systems, and analysis of topological states in this setting.
5. Numerical codes for moiré systems
6. Theory of nonlinear spectroscopy of confined phases, random magnets, heavy fermions, and exactly-solvable spin systems
7. Quasiparticle decay and dynamics in CoNb2O6 and other nonsymmorphic symmetry-breaking chains.
8. Further progress on classification and numerical techniques.
Different possible surface terminations for higher-order topological phases.
New model based on glide symmetry can correctly capture quasiparticle breakdown in CoNb2O6.