Quantum Matter

The study of spectral statistics is of importance due to its universality and utility as a robust diagnostic of quantum chaos. For closed many-body quantum chaotic systems, I will present two results: (i) a quantum-classical mapping that connects the Thouless time, which characterizes the onset of RMT of the spectral form factor (SFF); and the spectral gap of a dual classical stochastic system; (ii) a set of Lyapunov exponents which characterize the spectral statistics in the thermodynamic limit. For open quantum systems with complex spectra, I will propose and analyze a generalized SFF, and show that dissipative quantum chaotic systems display a “dip-ramp-plateau” behaviour with a quadratic ramp.

Kitaev quantum spin liquids (QSLs) are exotic states of matter that are predicted to host Majorana fermions and gauge flux excitations. However, so far all known Kitaev QSL candidates are known to have appreciable non-Kitaev interactions that pushes these systems far from the QSL regime. Co based magnets have been proposed to be perhaps a more ideal platform for realizing Kitaev QSLs. In this talk I will show evidence for a Kitaev interactions in both the quasi-one-dimensional ferromagnet CoNb2O6 as well as the hexagonal magnet BaCo2(AsO4). Although it is usually believed to be the best material realization of a 1D Ising chain, by combining terahertz spectroscopy and calculations we have shown that CoNb2O6 is well described by a model with bond-dependent interactions. We call this model the ‘twisted Kitaev chain’, as these interactions are similar to those of the honeycomb Kitaev spin liquid. The ferromagnetic ground state of CoNb2O6 arises from the compromise between two axes. Owing to this frustration, even at zero field domain walls have quantum motion, which is described by the celebrated Su–Schrieffer–Heeger model of polyacetylene and shows rich behavior as a function of field. Most recently, we have shown also that the honeycomb cobalt-based Kitaev QSL candidate, BaCo2(AsO4)2, has dominant Kitaev interactions. Due to only small non-Kitaev terms a magnetic continuum consistent with Majorana fermions and the existence of a Kitaev QSL can be induced by a small out-of-plane-magnetic field. Our results demonstrate BaCo2(AsO4)2 as a far more ideal version of Kitaev QSL compared with other candidates.

C. M Morris et al. "Hierarchy of bound states in the one-dimensional ferromagnetic Ising chain CoNb2O6 investigated by high-resolution time-domain terahertz spectroscopy.” Phys. Rev. Lett. 112.13 137403 (2014).

C.M. Morris et al. “Duality and domain wall dynamics in a twisted Kitaev chain”, Nature Physics

volume 17, pages 832–836 (2021).

X. Zhang, et al., "In- and out-of-plane field induced quantum spin-liquid states in a more ideal Kitaev material: BaCo2(AsO4)”, https://arxiv.org/abs/2106.13418

Zoom Link: https://pitp.zoom.us/meeting/register/tJcqc-ihqzMvHdW-YBm7mYd_XP9Amhypv5vO

Traditionally, quantum many-body theory has focussed on ground states and equilibrium properties of spatially extended systems, such as electrons and spins in crystalline solids. In recent years “noisy intermediate scale quantum computers” (NISQ) have emerged, providing new opportunities for controllable non-equilibrium many-body systems. In such dynamical quantum systems the inexorable growth of non-local quantum entanglement is expected, but monitoring (by making projective measurements) can compete against entanglement growth. In this talk I will overview theoretical work exploring the behavior of “monitored” quantum circuits, which can exhibit a novel quantum dynamical phase transition between a weak measurement phase and a quantum Zeno phase, the former which we characterize in detail. Accessing such physics in the lab is challenged by the need for post-selection, which might be circumnavigated by decoding using active error correction, conditioned on the measurement outcomes, as will be described in systems with Z2 symmetry.

Zoom Link: https://pitp.zoom.us/meeting/register/tJcqc-ihqzMvHdW-YBm7mYd_XP9Amhypv5vO

In this talk, I will present a general approach to obtain effective field theories for topological crystalline insulators whose low-energy theories are described by massive Dirac fermions. We show that these phases are characterized by the responses to spatially dependent mass parameters with interfaces. These mass interfaces implement the dimensional reduction procedure such that the state of interest is smoothly deformed into a network of defects (dubbed topological crystal), where each defect supports a short-ranged entangled state. Effective field theories are obtained by integrating out the massive Dirac fermions, and various quantized topological terms are uncovered. I will describe how to apply this strategy through a few simple examples and comment on the relation to the topological elasticity theory. 

Twisted bilayer graphene (TBG) realizes an exquisitely tunable, strongly interacting system featuring superconductivity and various correlated insulating states. In this talk I will introduce gate-defined wires in TBG as an enticing platform for Majorana-based fault-tolerant qubits. Our proposal notably relies on “internally” generated superconductivity in TBG – as opposed to “external” superconducting proximity effects commonly employed in Majorana devices – and may operate even at zero magnetic field. I will also describe how electrical measurements of gate-defined wires can reveal the nature of correlated insulators and shed light on the Cooper-pairing mechanism in TBG.

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The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatments, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less complex and thus describable with (classical) effective theories.

I will discuss how unsupervised learning can detect the local complexity of states. This approach can be used as a probe of scrambling and thermalization in chaotic quantum systems or to assign the local complexity of density matrices in open setups without knowing the corresponding Hamiltonian or Liouvillian. The analysis actually allows for the reconstruction of Hamiltonian operators or even noise-type that might be contaminating the measurements. Our approach is an ideal diagnostics tool for data obtained from (noisy) quantum simulators because it requires only practically accessible local observations. For example, it would be perfectly suited to detect the many-body localization (MBL) transition or integrability effects from the experimental snapshots obtained with cold atoms.

If time permits, I will mention other ways to detect properties of MBL transition in weakly open and driven setups and the advantages of such an unconventional approach.

M. Schmitt and Z. Lenarcic, arXiv:2102.11328.

Z. Lenarcic, O. Alberton, A. Rosch and E. Altman, PRL 125, 116601 (2020).

In this work, we introduce and study "hybrid" fracton orders, especially though a family of exactly solvable models. The hybrid fracton orders exhibit both the phenomenology of a conventional 3d topological ordered phase and a fracton phase. There are simple yet non-trivial fusion and braiding between the excitations between the two kinds. One example is the hybrid order of the Z2 topological order with the Z2 Xcube order, in which the fracton excitations fuse into the toric code charge, and in turn, the flux loop of the toric code can fuse into various lineon excitations. In the same way there is a hybrid ordered phase of Haah's code and the 3d toric code. Proliferating certain gapped excitations in these hybrid orders can drive a phase transition into either a fracton order or a conventional 3d topological phase. 

Reference. ArXiv 2102.09555

The entanglement pattern of a quantum many-body system can be characterized by quasiparticles and emergent gauge fields, much like those found in Maxwell's theory. My talk begins with the basic aspects of symmetry fractionalization and emergent gauge fields in strongly correlated systems. I will further extend this paradigm into a new type of quantum many-body state, dubbed "fracton phase," from a quantum melting transition of plaquette paramagnetic crystals. These exotic states contain fractionalized sub-dimensional quasiparticles with constraint motion and emergent higher-rank gauge fields. Such constraint dynamics of the quasiparticles bring about an intriguing Bose metal phase with quasi-long range order and yields non-local quantum entanglement. In particular, the key peculiarities of this phase is the UV/IR mixing, where the short wavelength physics controls the low energy theory and hence challenges the standard notion of the renormalization group perspective.

Metals are ubiquitous in nature. One would like to determine the effective field theory that describe the low-energy physics of a metal. Many materials are successfully described by the so-called "Fermi liquid theory", but there is also much interest in "non-Fermi liquid metals" that evade such a description.

In this talk, I will present a very general perspective on metals that strongly constrains the possible effective field theories. The discussion is based on powerful theoretical concepts such as emergent symmetries and anomalies. From this perspective, combined with experimental observations, one can derive strong and unexpected conclusions about the nature of a particular kind of non-Fermi liquid metal, the "strange metal" observed in doped cuprates.

High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat  the electron interactions.  Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity.  In 1992 Hatsugai and Khomoto wrote down a momentum-space model for a Mott insulator which is safe to say was largely overlooked, their paper garnering just 21 citations (6 due to our group).  I will show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper's instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity.  The properties of the superconducting state differ drastically from that of the standard BCS theory.  The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state.

Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.

[1] https://www.nature.com/articles/s41567-020-0988-4.

Twisted bilayer graphene (tBLG) is a host to a variety of electronic phases, most notably superconductivity when doped away from putative correlated insulator phases. In order to understand the nature of those phases, numerical simulations such as Hartree-Fock calculation and density matrix renormalization group (DMRG) techniques are essential.

Due to the long-range Coulomb interaction and its fragile topology, however, tBLG is difficult to study with standard DMRG techniques.

In this work, we present how a recently developed MPO compression algorithm can be used to make the problem tractable, and how 1D Wannier localization can be used to circumvent the fragile topology.

As a test case, we apply this technique to the toy model of spinless/single-valley model of tBLG. We find that the ground state is essentially a k-space Slater determinant, confirming the validity of previous Hartree-Fock calculations. If time permits, I will also present our ongoing effort to apply this technique to spinful/valleyful model for tBLG.

The quest for non-Abelian quasiparticles has inspired decades of experimental and theoretical efforts. Among their clearest signatures is a thermal Hall conductance with quantized half-integer value. Such a value was indeed recently observed in a quantum-Hall system at ν=5/2 and in the magnetic insulator α-RuCl3. I will explain that a non-topological "thermal metal" phase that forms due to quenched disorder may disguise as a non-Abelian phase by well approximating the trademark quantized thermal Hall response. Remarkably, the quantization here improves with temperature, in contrast to fully gapped systems. In my talk, I will provide analytical and numerical evidence for this effect and discuss its possible implications for the aforementioned experiments.