Research areas

Eigenstate order	Topological materials
Floquet physics	Nonequilibrium phases and phase transition
Frustrated magnets and fractionalization	Many-body localization
Quantum information

In the Condensed Matter Division we are interested in a broad range of collective phenomena. These can be grouped under three central umbrellas of quantum matter, new kinds of order and quantum dynamics, while still substantial interconnections naturally emerge, see the illustration in the figure above.

A key scope of research is the identification and theoretical description of new kinds of order ranging from unconventional phases such as quantum spin liquids appearing in frustrated magnets to topological matter. These phases often cannot be described by local order parameters but rather entail peculiar entanglement properties linking condensed matter theory directly to quantum information concepts.

The far from equilibrium regime on the other hand, nowadays experimentally accessible in so-called quantum simulators, naturally provides the room for novel quantum states because constraints by equilibrium principles such as the equal a priori probability in the microcanonical ensemble are lifted generically. Prominent examples include the many-body localized phase or eigenstate phases in periodically driven Floquet systems such as discrete time crystals. Detailed descriptions of the individual research topics can be found under the respective embedded links in the figure above.

Interactions and Mobility Edges: Observing the Generalized Aubry-André Model

F. A. An, K. Padavić, E. J. Meier, S. Hegde, S. Ganeshan, J. H. Pixley, S. Vishveshwara, and B. Gadway

Using synthetic lattices of laser-coupled atomic momentum modes, we experimentally realize a recently proposed family of nearest-neighbor tight-binding models having quasiperiodic site energy modulation that host an exact mobility edge protected by a duality symmetry. These one- dimensional tight-binding models can be viewed as a generalization of the well-known Aubry- André model, with an energy-dependent selfduality condition that constitutes an analytical mobility edge relation. By adiabatically preparing low and high energy eigenstates of this model system and performing microscopic measurements of their participation ratio, we track the evolution of the mobility edge as the energy-dependent density of states is modified by the model’s tuning parameter. Our results show strong deviations from single-particle predictions, consistent with attractive interactions causing both enhanced localization of the lowest energy state due to self-trapping and inhibited localization of high energy states due to screening. This study paves the way for quantitative studies of interaction effects on self-duality induced mobility edges.

Phys. Rev. Lett. 126, 040603 (2020)

Quantum paracrystalline shear modes of the electron liquid

J. Y. Khoo, P.-Y. Chang, F. Pientka, I. Sodemann

Unlike classical fluids, a quantum Fermi liquid can support a long-lived and propagating shear sound wave at arbitrarily small wave vectors and frequencies, reminiscent of the transverse sound in crystals, despite lacking any form of long-range crystalline order. This mode is expected to be present in moderately interacting metals where the quasiparticle mass is renormalized to be more than twice the bare mass in two dimensions (2D), but it has remained undetected because it is hard to excite since it does not involve charge density fluctuations, in contrast to the conventional plasma mode. In this work we propose a strategy to excite and detect this unconventional mode in clean metallic channels. We show that the shear sound is responsible for the appearance of sharp dips in the ac conductance of narrow channels at resonant frequencies matching its dispersion. The liquid resonates while minimizing its dissipation in an analogous fashion to a sliding crystal. Ultraclean 2D materials that can be tuned toward the Wigner crystallization transition such as silicon metal-oxide-semiconductor field-effect transistors, MgZnO/ZnO, p- GaAs, and AlAs quantum wells are promising platforms to experimentally discover the shear sound.

Phys. Rev. B 102, 085437 (2020)

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Fragile extended phases in the log-normal Rosenzweig-Porter model

I. M. Khaymovich, V. E. Kravtsov, B. L. Altshuler, and L. B. Ioffe

In this paper, we suggest an extension of the Rosenzweig-Porter (RP) model, the LN-RP model, in which the off-diagonal matrix elements have a wide, log-normal distribution. We argue that this model is more suitable to describe a generic many-body localization problem. In contrast to RP model, in LN-RP model, a fragile weakly ergodic phase appears that is characterized by broken basis-rotation symmetry which the fully ergodic phase, also present in this model, strictly respects in the thermodynamic limit. Therefore, in addition to the localization and ergodic transitions in LN-RP model, there exists also the transition between the two ergodic phases (FWE transition). We suggest new criteria of stability of the nonergodic phases that give the points of localization and ergodic transitions and prove that the Anderson localization transition in LN-RP model involves a jump in the fractal dimension of the egenfunction support set. We also formulate the criterion of FWE transition and obtain the full phase diagram of the model. We show that truncation of the log-normal tail shrinks the region of weakly ergodic phase and restores the multifractal and the fully ergodic phases.

Phys. Rev. Research 2, 043346 (2020)

Odd elasticity

C. Scheibner, A. Souslov, D. Banerjee, P. Surówka, W. T. M. Irvine, V. Vitelli

A passive solid cannot do work on its surroundings through any quasistatic cycle of deformations. This property places strong constraints on the allowed elastic moduli. In this Article, we show that static elastic moduli altogether absent in passive elasticity can arise from active, non- conservative microscopic interactions. These active moduli enter the antisymmetric (or odd) part of the static elastic modulus tensor and quantify the amount of work extracted along quasistatic strain cycles. In two-dimensional isotropic media, two chiral odd-elastic moduli emerge in addition to the bulk and shear moduli. We discuss microscopic realizations that include networks of Hookean springs augmented with active transverse forces and non-reciprocal active hinges. Using coarse-grained microscopic models, numerical simulations and continuum equations, we uncover phenomena ranging from auxetic behaviour induced by odd moduli to elastic wave propagation in overdamped media enabled by self-sustained active strain cycles. Our work sheds light on the non-Hermitian mechanics of two- and three-dimensional active solids that conserve linear momentum but exhibit a non-reciprocal linear response.

Nature Physics 16, 475 (2020)

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Many-body Delocalization via Emergent Symmetry

N. S. Srivatsa, R. Moessner, and A. E. B. Nielsen

Many-body localization (MBL) provides a mechanism to avoid thermalization in many-body quantum systems. Here, we show that an emergent symmetry can protect a state from MBL. Specifically, we propose a Z₂ symmetric model with nonlocal interactions, which has an analytically known, SU(2) invariant, critical ground state. At large disorder strength, all states at finite energy density are in a glassy MBL phase, while the lowest energy states are not. These do, however, localize when a perturbation destroys the emergent SU(2) symmetry. The model also provides an example of MBL in the presence of nonlocal, disordered interactions that are more structured than a power law. Finally, we show how the protected state can be moved into the bulk of the spectrum.

Phys. Rev. Lett. 125, 240401 (2020)

Non-perturbative terahertz high-harmonic generation in the three- dimensional Dirac semimetal Cd₃As₂

S. Kovalev, R. M. A. Dantas, S. Germanskiy, J.-C. Deinert, B. Green, I. Ilyakov, N. Awari, M. Chen, M. Bawatna, J. Ling, F. Xiu, P. H. M. van Loosdrecht, P. Surówka, T. Oka, Z. Wang

Harmonic generation is a general characteristic of driven nonlinear systems, and serves as an efficient tool for investigating the fundamental principles that govern the ultrafast nonlinear dynamics. Here, we report on terahertz-field driven high-harmonic generation in the three- dimensional Dirac semimetal Cd₃As₂ at room temperature. Excited by linearly-polarized multi-cycle terahertz pulses, the third-, fifth-, and seventh-order harmonic generation is very efficient and detected via time-resolved spectroscopic techniques. The observed harmonic radiation is further studied as a function of pump-pulse fluence. Their fluence dependence is found to deviate evidently from the expected power-law dependence in the perturbative regime. The observed highly non-perturbative behavior is reproduced based on our analysis of the intraband kinetics of the terahertz-field driven nonequilibrium state using the Boltzmann transport theory. Our results indicate that the driven nonlinear kinetics of the Dirac electrons plays the central role for the observed highly nonlinear response.

Nat. Commun. 11, 2451 (2020)

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