Suspended carbon nanotubes are known to support self-driven oscillations due to electromechanical feedback under certain conditions, including low temperatures and high mechanical quality factors. Prior reports identified signatures of such oscillations in Kondo or high-bias transport regimes. Here, we observe self-driven oscillations that give rise to significant conduction in normally Coulomb blockaded low-bias transport. Using a master equation model, the self-driving is shown to result from strongly energy-dependent electron tunneling, and the dependencies of transport features on bias, gate voltage, and temperature are well reproduced.

We study the exchange interaction between two hole-spin qubits in a double quantum dot setup in a silicon nanowire in the presence of magnetic and electric fields. Based on symmetry arguments we show that there exists an effective spin that is conserved even in highly anisotropic semiconductors, provided that the system has a twofold symmetry with respect to the direction of the applied magnetic field. This finding facilitates the definition of qubit basis states and simplifies the form of exchange interaction for two-qubit gates in coupled quantum dots. If the magnetic field is applied along a generic direction, cubic anisotropy terms act as an effective spin-orbit interaction introducing novel exchange couplings even for an inversion symmetric setup. Considering the example of a silicon nanowire double dot, we present the relative strength of these anisotropic exchange interaction terms and calculate the fidelity of the $\sqrt{\text{SWAP}}$ gate. Furthermore, we show that the anisotropy-induced spin-orbit effects can be comparable to that of the direct Rashba spin-orbit interaction for experimentally feasible electric field strengths.

Dirac materials are of great interest as condensed matter realizations of the Dirac and Weyl equations. In particular, they serve as a starting point for the study of topological phases. This physics has been extensively studied in electronic systems such as graphene, Weyl, and Dirac semimetals. In contrast, recent studies have highlighted several examples of Dirac-like cones in collective excitation spectra, viz. in phonon, magnon, and triplon bands. These cannot be directly related to the Dirac or Weyl equations as they are bosonic in nature with pseudounitary band bases. We address this issue by constructing a generic deformation scheme that maps any fermionic Hamiltonian and its spectrum to that of a bosonic problem. In particular, we show that any Dirac-like equation can be deformed into a suitable bosonic form. The resulting bosonic spectra bear a two-to-one relation to that of the parent Dirac system. Their dispersions inherit several interesting properties including conical band touching points and a gap-opening role for ‘mass’ terms. The relationship also extends to the band eigenvectors with the bosonic states carrying the same Berry connections as the parent fermionic states. The bosonic bands thus inherit topological character as well. If the parent fermionic system has nontrivial topology that leads to midgap surface states, the bosonic analog also hosts surface states that lie within the corresponding band gap. The proposed bosonic Dirac structure appears in several known models. In materials, it is realized in ${\mathrm{Ba}}_2{\mathrm{CuSi}}_2{\mathrm{O}}_6{\mathrm{Cl}}_2$ and possibly in ${\mathrm{CoTiO}}_3$ as well as in paramagnetic honeycomb ruthenates. Our results allow for a rigorous understanding of Dirac phononic and magnonic systems and enable concrete predictions, e.g., of surface states in magnonic topological insulators and Weyl semimetals.

We consider the long-time limit of out-of-time-order correlators (OTOCs) in two classes of quantum lattice models with time evolution governed by local unitary quantum circuits and maximal butterfly velocity $v_B=1$. Using a transfer matrix approach, we present analytic results for the long-time value of the OTOC on and inside the light cone. First, we consider “dual-unitary” circuits with various levels of ergodicity, including the integrable and nonintegrable kicked Ising model, where we show exponential decay away from the light cone and relate both the decay rate and the long-time value to those of the correlation functions. Second, we consider a class of kicked $\mathit{XY}$ models similar to the integrable kicked Ising model, again satisfying $v_B=1$, highlighting that maximal butterfly velocity is not exclusive to dual-unitary circuits.

We provide a simple and predictive random-matrix framework that naturally generalizes Page's law for ergodic many-body systems by incorporating a finite entanglement localization length. By comparing a highly structured one-dimensional model to a completely unstructured model and a physical system, we uncover a remarkable degree of universality, suggesting that the effective localization length is a universal combination of model parameters up until it drops down to the microscopic scale.

We numerically prove photoinduced $\eta$-pairing in a half-filled fermionic Hubbard chain at both zero and finite temperature. The result, obtained by combining the matrix-product-state based infinite time-evolving block decimation technique and the purification method, applies to the thermodynamic limit. Exciting the Mott insulator by a laser electric field docked on via the Peierls phase, we track the time evolution of the correlated many-body system and determine the optimal parameter set for which the nonlocal part of the $\eta$-pair-correlation function becomes dominant during the laser pump at zero and low temperatures. These correlations vanish at higher temperatures and long times after pulse irradiation. In the high laser frequency strong Coulomb coupling regime we observe a remnant enhancement of the Brillouin-zone boundary pair-correlation function also at high temperatures, if the Hubbard interaction is about a multiple of the laser frequency, which can be attributed to an enhanced double occupancy in the virtual Floquet state.

Light-matter coupling involving classical and quantum light offers a wide range of possibilities to tune the electronic properties of correlated quantum materials. Two paradigmatic results are the dynamical localization of electrons and the ultrafast control of spin dynamics, which have been discussed within classical Floquet engineering and in the deep quantum regime where vacuum fluctuations modify the properties of materials. Here we discuss how these two extreme limits are interpolated by a cavity which is driven to the excited states. In particular, this is achieved by formulating a Schrieffer-Wolff transformation for the cavity-coupled system, which is mathematically analogous to its Floquet counterpart. Some of the extraordinary results of Floquet engineering, such as the sign reversal of the exchange interaction or electronic tunneling, which are not obtained by coupling to a dark cavity, can already be realized with a single-photon state (no coherent states are needed). The analytic results are verified and extended with numerical simulations on a two-site Hubbard model coupled to a driven cavity mode. Our results generalize the well-established Floquet engineering of correlated electrons to the regime of quantum light. This opens up a pathway of controlling properties of quantum materials with high tunability and low energy dissipation.

Quantum many-body systems described by Lagrangian path integrals can realize many different topological phases of matter. One of the most important problems in condensed-matter physics is to extract topological invariants from the Lagrangian and to determine the topological order in the systems. In this paper, we suggest a general solution to this problem. Given a path integral on space-time lattice $C^{d+1}$ that describes a short-range correlated (i.e., gapped) system, we design systematic ways to extract topological invariants. For example, we show how to use nonuniversal partition functions $Z\left(C^{2+1}\right)$ on several space-time lattices with related topologies to extract ${\left(M_f\right)}_{11}$ and $\text{Tr}\left(M_f\right)$, where $M_f$ is a representation of the modular group $\text{SL}(2,\mathbf{Z})$, a topological invariant that characterizes ($2+1$)-dimensional topological orders. Our approach is guided by a notion of quantum volume. A path integral gives rise to a wave function $|\mathrm{\Psi }\rangle$ on the boundary of ($d+1$)-dimensional space-time $C^{d+1}$. We show that $V=\text{ln}\sqrt{\langle \mathrm{\Psi }|\mathrm{\Psi }\rangle }$ satisfies the inclusion-exclusion property $\frac{V(A\cup B)+V(A\cap B)}{V\left(A\right)+V\left(B\right)}=1$ and behaves like a volume of the space-time $C^{d+1}$ in the thermodynamics limit if the system is short range correlated. This leads to a proposal that the vector $|\mathrm{\Psi }\rangle$ itself is the quantum volume of the space-time $C^{d+1}$. The subleading term of thermodynamics limit gives rise to the topological invariants.

Modern theory of electric polarization is formulated by the Berry phase, which, when quantized, leads to topological phases of matter. Such a formulation has recently been extended to higher electric multipole moments, through the discovery of the so-called quadupole topological insulator. It has been established by a classical electromagnetic theory that in a two-dimensional material the quantized properties for the quadupole topological insulator should satisfy a basic relation. Here we discover a new type of quadrupole topological insulator (dubbed type-II) that violates this relation due to the breakdown of the correspondence that a Wannier band and an edge energy spectrum close their gaps simultaneously. We find that, similarly to the previously discovered (referred to as type-I) quadrupole topological insulator, the type-II hosts topologically protected corner states carrying fractional corner charges. However, the edge polarizations only occur at a pair of boundaries in the type-II insulating phase, leading to the violation of the classical constraint. We demonstrate that such new topological phenomena can appear from quench dynamics in non-equilibrium systems, which can be experimentally observed in ultracold atomic gases. We also propose an experimental scheme with electric circuits to realize such a new topological phase of matter. The existence of the new topological insulating phase means that new multipole topological insulators with distinct properties can exist in broader contexts beyond classical constraints.

The underscreened Kondo lattice consisting of a single twofold degenerate conduction band and a crystalline electric-field (CEF) split $4f$-electron quasiquartet has nonconventional quasiparticle dispersions obtained from the constrained mean-field theory. An additional genuinely heavy band is found in the main hybridization band gap of the upper and lower hybridzed bands whose heavy effective mass is controled by the CEF splitting. Its presence should profoundly influence the dynamical optical and magnetic response functions. In the former the onset of the optical conductivity is not the main hybridization energy but the much lower Kondo energy scale which appears in the direct transitions to the additional heavy band. The dynamical magnetic response is also strongly modified by the in-gap heavy band which can lead to unconventional resonant excitations that may be interpreted as coherent CEF-Kondo lattice magnetic exciton bands. Their instability at low temperature signifies the onset of induced excitonic magnetism in the underscreened Kondo lattice.

The Sachdev-Ye-Kitaev (SYK) model has emerged as a new paradigm of non-Fermi-liquid behavior. Here we investigate a possibility of having a superconducting off-diagonal long-range order (ODLRO) and a pseudogap phase within the SYK framework. We found that ODLRO may be established in a spin-1/2 version of the model with the time-reversal invariance and an extra attractive interaction. If the latter is taken as the on-site negative $U$ Hubbard term, it leads to the pseudogap phase at $U<U_c$ dominated by quantum fluctuations of local phases. These fluctuations are described by a quantum version of the Kuramoto model, traditionally employed to illustrate synchronization of classical nonlinear oscillators. In the opposite limit of large $U$, the SYK $+$ Hubbard model is approaching a certain generalization of the integrable Richardson model. We present exact diagonalization studies, along with analytic solutions of the aforementioned limiting cases. We also discuss possible holographic interpretations of the model, ODLRO, and the pseudogap.

The relaxation properties of supercooled ${\mathrm{As}}_x{\mathrm{S}}_{100-x}$ liquids are investigated using a combination of infrared photon correlation spectroscopy and topological constraint theory. Results reveal two channels of relaxation for sulfur-rich compositions that manifest by an unusual profile in the density-density autocorrelation function involving two typical timescales. This indicates a reduced temperature-dependent dynamics for one of the channels associated with a sulfur-rich segregated nanoscale phase that furthermore displays a low liquid fragility. Conversely, the dynamics of the emerging cross-linked As-S network is associated with a growth of the glass transition temperature with As content. These results can be quantitatively understood from topological constraint theory applied to a phase separated network for which a dedicated constraint enumeration must be achieved. The vanishing of this peculiar behavior occurs close to the reported isostatic reversibility window observed at the glass transition.

Topological entanglement entropy has been extensively used as an indicator of topologically ordered phases. We study the conditions needed for two-dimensional topologically trivial states to exhibit spurious contributions that contaminate topological entanglement entropy. We show that, if the state at the boundary of a subregion is a stabilizer state, then it has a nonzero spurious contribution to the region if and only if the state is in a nontrivial one-dimensional $G_1\times G_2$ symmetry-protected-topological (SPT) phase under an on-site symmetry. However, we provide a candidate of a boundary state that has a nonzero spurious contribution but does not belong to any such SPT phase.

Universality is a powerful concept that arises from the divergence of a characteristic length scale. For condensed matter systems, this length scale is typically the correlation length, which diverges at critical points separating two different phases. Few-particle systems exhibit a simpler form of universality when the $s$-wave scattering length diverges. A prominent example of universal phenomena is the emergence of an infinite tower of three-body bound states obeying discrete scale invariance, known as the Efimov effect, which has been subject to extensive research in chemical, atomic, nuclear, and particle physics. In principle, these universal phenomena can also emerge in the excitation spectrum of condensed matter systems, such as quantum magnets [Y. Nishida, Y. Kato, and C. Batista, Nat. Phys. 9, 93 (2013)]. However, the limited tunability of the effective interparticle interaction relative to the kinetic energy has precluded so far their observation. Here, we demonstrate that a high degree of magnetic field induced tunability can also be achieved in quantum magnets with strong spin-orbit coupling: A two-magnon resonance condition can be achieved in ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ with a field of $\sim 13$ T along the [110] direction, which leads to the formation of Efimov states in the three-magnon spectrum of this material. Raman scattering experiments can reveal the field-induced two-magnon resonance, as well as the Efimov three-magnon bound states that emerge near the resonance condition.

In the study of $\mathcal{P}\mathcal{T}$-symmetric quantum systems with non-Hermitian perturbations, one of the most important questions is whether eigenvalues stay real or whether $\mathcal{P}\mathcal{T}$ symmetry is spontaneously broken when eigenvalues meet. A particularly interesting set of eigenstates is provided by the degenerate ground-state subspace of systems with topological order. In this paper, we present simple criteria that guarantee the protection of $\mathcal{P}\mathcal{T}$ symmetry and, thus, the reality of the eigenvalues in topological many-body systems. We formulate these criteria in both geometric and algebraic form and demonstrate them using the toric code and several different fracton models as examples. Our analysis reveals that $\mathcal{P}\mathcal{T}$ symmetry is robust against a remarkably large class of non-Hermitian perturbations in these models; this is particularly striking in the case of fracton models due to the exponentially large number of degenerate states.

We investigate the entanglement-renormalization group flows of translation-invariant topological stabilizer models in three dimensions. Fracton models are observed to bifurcate under entanglement renormalization, generically returning at least one copy of the original model. Based on this behavior, we formulate the notion of bifurcated equivalence for fracton phases, generalizing foliated fracton equivalence. The notion of quotient superselection sectors is also generalized accordingly. We calculate bifurcating entanglement-renormalization group flows for a wide range of examples and, based on those results, propose conjectures regarding the classification of translation-invariant topological stabilizer models in three dimensions.

Recent studies found that the diffusive transport of conserved quantities in nonintegrable many-body systems has an imprint on quantum entanglement: while the von Neumann entropy of a state grows linearly in time $t$ under a global quench, all $n\mathrm{th}$ Rényi entropies with $n>1$ grow with a diffusive scaling $\sqrt{t}$. To understand this phenomenon, we introduce an amplitude $A\left(t\right)$, which is the overlap of the time evolution operator $U\left(t\right)$ of the entire system with the tensor product of the two evolution operators of the subsystems of a spatial bipartition. As long as $\left|A\left(t\right)\right|\ge e^{-\sqrt{Dt}}$, which we argue holds true for generic diffusive nonintegrable systems, all $n\mathrm{th}$ Rényi entropies with $n>1$ (annealed averaged over initial product states) are bounded from above by $\sqrt{t}$. We prove the following inequality for the disorder average of the amplitude, $\overline{\left|A\right(t\left)\right|}\ge e^{-\sqrt{Dt}}$, in a local spin-$\frac{1}{2}$ random circuit with a $\text{U}\left(1\right)$ conservation law by mapping to the survival probability of a symmetric exclusion process. Furthermore, we numerically show that the typical decay behaves asymptotically, for long times, as $\left|A\left(t\right)\right|\sim e^{-\sqrt{Dt}}$ in the same random circuit as well as in a prototypical nonintegrable model with diffusive energy transport but no disorder.

One of the unique features of Dirac Fermions is pseudodiffusive transport by evanescent modes at low Fermi energies when disorder is low. At higher Fermi energies, i.e., charge carrier densities, the electrical transport is diffusive in nature and the propagation occurs via plane waves. In this study, we report the detection of such evanescent modes in the surface states of topological insulator through $1/f$ noise for the first time. While signatures of pseudodiffusive transport have been seen experimentally in graphene, such behavior is yet to be observed explicitly in any other system with a Dirac dispersion. To probe this, we have studied $1/f$ noise in topological insulators as a function of gate voltage, and temperature. Our results show a nonmonotonic behavior in $1/f$ noise as the gate voltage is varied, suggesting a crossover from pseudodiffusive to diffusive transport regime in mesoscopic topological insulators. The temperature dependence of noise points towards conductance fluctuations from quantum interference as the dominant source of the noise in these samples.

Critical phenomena arise ubiquitously in various contexts of physics, from condensed matter, high-energy physics, cosmology, to biological systems, and consist of slow and long-distance fluctuations near a phase transition or critical point. Usually, these phenomena are associated with the softening of a massive mode. Here, we show that a non-Hermitian-induced mechanism of critical phenomena that does not fall into this class can arise in the steady state of generic driven-dissipative many-body systems with coupled binary order parameters such as exciton-polariton condensates and driven-dissipative Bose-Einstein condensates in a double-well potential. The criticality of this “critical exceptional point” is attributed to the coalescence of the collective eigenmodes that convert all the thermal-and-dissipative-noise-activated fluctuations to the Goldstone mode, leading to anomalously giant phase fluctuations that diverge at spatial dimensions $d\le 4$. Our dynamic renormalization group analysis shows that this gives rise to a strong-coupling fixed point at dimensions as high as $d<8$ associated with a universality class beyond the classification by Hohenberg and Halperin, indicating how anomalously strong the many-body corrections are at this point. We find that this anomalous enhancement of many-body correlation is due to the appearance of a sound mode at the critical exceptional point despite the system's dissipative character.

We present random quantum circuit models for nonunitary quantum dynamics of free fermions in one spatial dimension. Numerical simulations reveal that the dynamics tends toward steady states with logarithmic violations of the entanglement area law and power law correlation functions. Moreover, starting with a short-range entangled many-body state, the dynamical evolution of entanglement and correlations quantitatively agrees with the predictions of two-dimensional conformal field theory with a spacelike time direction. We argue that this behavior is generic in nonunitary free quantum dynamics with time-dependent randomness, and we show that the emergent conformal dynamics of two-point functions arises out of a simple “nonlinear master equation.”