Many-body Resonances Research Articles

Phenomenology of the Prethermal Many-Body Localized Regime.

The dynamical phase diagram of interacting disordered systems has seen substantial revision over the past few years. Theory must now account for a large prethermal many-body localized regime in which thermalization is extremely slow, but not completely arrested. We derive a quantitative description of these dynamics in short-ranged one-dimensional systems using a model of successive many-body resonances. The model explains the decay timescale of mean autocorrelators, the functional form of the decay-a stretched exponential-and relates the value of the stretch exponent to the broad distribution of resonance timescales. The Jacobi method of matrix diagonalization provides numerical access to this distribution, as well as a conceptual framework for our analysis. The resonance model correctly predicts the stretch exponents for several models in the literature. Successive resonances may also underlie slow thermalization in strongly disordered systems in higher dimensions, or with long-range interactions.

Many-Body Resonances in the Avalanche Instability of Many-Body Localization

Many-body localized (MBL) systems fail to reach thermal equilibrium under their own dynamics, even though they are interacting, nonintegrable, and in an extensively excited state. One instability toward thermalization of MBL systems is the so-called ``avalanche,'' where a locally thermalizing rare region is able to spread thermalization through the full system. The spreading of the avalanche may be modeled and numerically studied in finite one-dimensional MBL systems by weakly coupling an infinite-temperature bath to one end of the system. We find that the avalanche spreads primarily via strong many-body resonances between rare near-resonant eigenstates of the closed system. Thus we find and explore a detailed connection between many-body resonances and avalanches in MBL systems.

Soft dipole resonance in C8 and its isospin symmetry with He8

We investigate the soft dipole resonance in the proton-rich nucleus $_{6}^{8}\mathrm{C}_{2}$, which is a collective dipole oscillation of four valence protons against the $\ensuremath{\alpha}$ core, and discuss the isospin symmetry with the mirror nucleus $_{2}^{8}\mathrm{He}_{6}$. We use the $\ensuremath{\alpha}+N+N+N+N$ five-body cluster model and many-body resonances are obtained using the complex-scaling method. The ${1}^{\ensuremath{-}}$ resonance of $_{6}^{8}\mathrm{C}_{2}$ is confirmed at the excitation energy of 13 MeV with a large decay width of 24 MeV, and its structure is similar to the soft dipole resonance in $_{2}^{8}\mathrm{He}_{6}$, such as the configuration mixing and the spatial properties. These results indicate a good isospin symmetry in the soft dipole resonances of two nuclei with a common collective excitation of multiproton and multineutron, while the ground states of two nuclei show different properties due to the Coulomb repulsion of valence protons in $_{6}^{8}\mathrm{C}_{2}$, leading to the symmetry breaking. In conclusion, the appearance of the isospin symmetry differs depending on the states of $_{6}^{8}\mathrm{C}_{2}$ and $_{2}^{8}\mathrm{He}_{6}$.

Possible interpretation of the complex expectation values associated with resonances

We propose a possible scheme to interpret the complex expectation values associated with resonances having the complex eigenenergies. Using the Green's function for resonances, the expectation value is basically described by the Breit-Wigner distribution as a function of the real excitation energy. In the expression of the complex expectation values for resonances, the real part brings the integral value of the distribution, while the imaginary part produces the deviation from the Breit-Wigner distribution,which explains a shift of the peak in the strength from the resonance energy. We apply the present scheme to the several nuclear resonances of $^{12}$C including the Hoyle state, and neutron/proton-rich nuclei of $^6$He, $^6$Be, $^8$He, and $^8$C. In these nuclei, many-body resonances are obtained as the complex-energy eigenstates under the correct boundary condition using the complex scaling method, and their nuclear radii are uniquely evaluated. We discuss the peculiar energy dependence of the strength function of the square radius for the resonances in these nuclei.

Stable Many-Body Resonances in Open Quantum Systems

Periodically driven quantum many-body systems exhibit novel nonequilibrium states, such as prethermalization, discrete time crystals, and many-body localization. Recently, the general mechanism of fractional resonances has been proposed that leads to slowing the many-body dynamics in systems with both U(1) and parity symmetry. Here, we show that fractional resonance is stable under local noise models. To corroborate our finding, we numerically study the dynamics of a small-scale Bose–Hubbard model that can readily be implemented in existing noisy intermediate-scale quantum (NISQ) devices. Our findings suggest a possible pathway toward a stable nonequilibrium state of matter, with potential applications of quantum memories for quantum information processing.

Many-body parametric resonances in the driven sine-Gordon model

We study a quantum many-body variant of the parametric oscillator, by investigating the driven sine-Gordon model with a modulated tunnel coupling via a semi-classical Truncated Wigner Approximation (TWA). We first analyze the parametric resonant regime for driving protocols that retain our model gapped, and compare the TWA to a Time-Dependent Variational Principle (TDVP). We then turn to a drive which closes the gap, resulting in an enhanced energy absorption. While the TDVP approach breaks down in this regime, we can apply TWA to explore the dynamics of the mode-resolved energy density, and the higher-order correlations between modes in the prethermal heating regime. For weak driving amplitude, we find an exponentially fast energy absorption in the main resonant mode, while the heating of all remaining modes is almost perfectly suppressed on short time scales. At later times, the highly excited main resonance provides effective resonant driving terms for its higher harmonics through the non-linearities in the Hamiltonian, and gives rise to an exponentially fast heating in these particular modes. We capture the strong correlations induced by these resonant processes by evaluating higher order connected correlation functions. Our results can be experimentally probed in ultracold atomic settings, with parallel one-dimensional quasi-condensates in the presence of a modulated tunnel coupling.

Onset of many-body quantum chaos due to breaking integrability

Integrable quantum systems of finite size are generically robust against weak enough integrability-breaking perturbations, but become quantum chaotic and thermalizing if the integrability-breaking is strong enough. We argue that the onset of quantum chaos can be described as a Fock-space delocalization process, with the eigenstates of the integrable system being taken as the "Fock states". The integrability-breaking perturbation introduces hopping in this Fock space, and chaos sets in when this hopping delocalizes the many-body eigenstates in this space. Depending on the range of the dominant Fock-space hopping, delocalization can occur either through a crossover, or via a transition that becomes sharp in the appropriate large-system dynamic limit. In either case, the perturbation strength at the onset of chaos scales to zero in the usual thermodynamic limit, with a size-dependence that we estimate analytically and compute numerically for a few specific models. We also identify two intermediate finite-size-dependent regimes: There is generally an intermediate nonchaotic regime in which integrability is broken strongly enough to produce some system-wide many-body resonances but not enough to thermalize the system. In spatially extended systems (but not in quantum dots) there is also a crossover or transition between chaotic regimes where the ratio of the system size to the mean free path of the quasiparticles of the integrable system is small versus large compared to unity.

A constructive theory of the numerically accessible many-body localized to thermal crossover

The many-body localised (MBL) to thermal crossover observed in exact diagonalisation studies remains poorly understood as the accessible system sizes are too small to be in an asymptotic scaling regime. We develop a model of the crossover in short 1D chains in which the MBL phase is destabilised by the formation of many-body resonances. The model reproduces several properties of the numerically observed crossover, including an apparent correlation length exponent \nu=1ν=1, exponential growth of the Thouless time with disorder strength, linear drift of the critical disorder strength with system size, scale-free resonances, apparent 1/\omega1/ω dependence of disorder-averaged spectral functions, and sub-thermal entanglement entropy of small subsystems. In the crossover, resonances induced by a local perturbation are rare at numerically accessible system sizes LL which are smaller than a \lambdaλ. For L \gg \sqrt{\lambda}L≫λ (in lattice units), resonances typically overlap, and this model does not describe the asymptotic transition. The model further reproduces controversial numerical observations which Refs. claimed to be inconsistent with MBL. We thus argue that the numerics to date is consistent with a MBL phase in the thermodynamic limit.

Avalanches and many-body resonances in many-body localized systems

We numerically study both the avalanche instability and many-body resonances in strongly-disordered spin chains exhibiting many-body localization (MBL). We distinguish between a finite-size/time MBL regime, and the asymptotic MBL phase, and identify some "landmarks" within the MBL regime. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition, in infinite-length systems, occurs much deeper in the MBL regime than has been suggested by most previous studies. Our other landmarks involve system-wide resonances. We find that the effective matrix elements producing eigenstates with system-wide resonances are enormously broadly distributed. This means that the onset of such resonances in typical samples occurs quite deep in the MBL regime, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regime in to three subregimes: (i) at strongest disorder, typical samples do not have any eigenstates that are involved in system-wide many-body resonances; (ii) there is a substantial intermediate regime where typical samples do have such resonances, but the pair of eigenstates with the minimum spectral gap does not; and (iii) in the weaker randomness regime, the minimum gap is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain non-resonant and the system thus still appears MBL in many respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i).

Many-body localization with quasiperiodic driving

Sufficient disorder is believed to localize static and periodically-driven interacting chains. With quasiperiodic driving by $D$ incommensurate tones, the fate of this many-body localization (MBL) is unknown. We argue that randomly disordered MBL exists for $D=2$, but not for $D\geq 3$. Specifically, a putative two-tone driven MBL chain is neither destabilized by thermal avalanches seeded by rare thermal regions, nor by the proliferation of long-range many-body resonances. For $D\geq 3$, however, sufficiently large thermal regions have continuous local spectra and slowly thermalize the entire chain. En route, we generalize the eigenstate thermalization hypothesis to the quasiperiodically-driven setting, and verify its predictions numerically. Two-tone driving enables new topological orders with edge signatures; our results suggest that localization protects these orders indefinitely.

Partial thermalisation of a two-state system coupled to a finite quantum bath

The eigenstate thermalisation hypothesis (ETH) is a statistical characterisation of eigen-energies, eigenstates and matrix elements of local operators in thermalising quantum systems. We develop an ETH-like ansatz of a partially thermalising system composed of a spin-\tfrac{1}{2}12 coupled to a finite quantum bath. The spin-bath coupling is sufficiently weak that ETH does not apply, but sufficiently strong that perturbation theory fails. We calculate (i) the distribution of fidelity susceptibilities, which takes a broadly distributed form, (ii) the distribution of spin eigenstate entropies, which takes a bi-modal form, (iii) infinite time memory of spin observables, (iv) the distribution of matrix elements of local operators on the bath, which is non-Gaussian, and (v) the intermediate entropic enhancement of the bath, which interpolates smoothly between S = 0S=0 and the ETH value of S = \log 2S=log2. The enhancement is a consequence of rare many-body resonances, and is asymptotically larger than the typical eigenstate entanglement entropy. We verify these results numerically and discuss their connections to the many-body localisation transition.

Five-body resonances in He8 and C8 using the complex scaling method

We study many-body resonances in the neuron-rich $^{8}\mathrm{He}$ and the mirror proton-rich $^{8}\mathrm{C}$ using the $^{4}\mathrm{He}+N+N+N+N$ five-body model with the isospin $T=2$ system. Resonances are described with the complex energy eigenvalues as the Gamow states using the complex scaling method. In $^{8}\mathrm{He}$, we obtain five states in which four states are resonances, and in $^{8}\mathrm{C}$ all five states are resonances. We discuss the isospin-symmetry breaking dynamically induced by the Coulomb interaction in the energy spectra and decay widths of the resonances in two mirror nuclei. We predict the resonance energies and decay widths for the future experiments. We also investigate the configurations of valence nucleons above $^{4}\mathrm{He}$ in two nuclei with the $jj$ coupling scheme, and all the states dominantly have the $p$-shell configurations. From the configuration mixing, $^{8}\mathrm{He}$ and $^{8}\mathrm{C}$ give the similar results, which indicates the good symmetry in two nuclei.

Unitary Long-Time Evolution with Quantum Renormalization Groups and Artificial Neural Networks.

In this work, we combine quantum renormalization group approaches with deep artificial neural networks for the description of the real-time evolution in strongly disordered quantum matter. We find that this allows us to accurately compute the long-time coherent dynamics of large many-body localized systems in nonperturbative regimes including the effects of many-body resonances. Concretely, we use this approach to describe the spatiotemporal buildup of many-body localized spin-glass order in random Ising chains. We observe a fundamental difference to a noninteracting Anderson insulating Ising chain, where the order only develops over a finite spatial range. We further apply the approach to strongly disordered two-dimensional Ising models, highlighting that our method can be used also for the description of the real-time dynamics of nonergodic quantum matter in a general context.

The role of spin-flip assisted or orbital mixing tunneling on transport through strongly correlated multilevel quantum dot

Using the slave boson Kotliar-Ruckenstein approach (SBMFA) for N level Anderson model, we compare fully symmetric SU(N) Kondo resonances occurring for spin and orbital conserving tunneling with many-body resonances for the dot with broken symmetry caused by spin, orbital or full spin-orbital mixing. As a result of interorbital or spin flip processes new interference paths emerge, which manifests in the occurrence of antibonding Dicke like and bonding Kondo like resonances. The analytical expressions for linear conductances and linear temperature thermopower coefficient for arbitrary N are found.

Quantum critical behaviour at the many-body localization transition.

Phase transitions are driven by collective fluctuations of a system's constituents that emerge at a critical point1. This mechanism has been extensively explored for classical and quantum systems in equilibrium, whose critical behaviour is described by the general theory of phase transitions. Recently, however, fundamentally distinct phase transitions have been discovered for out-of-equilibrium quantum systems, which can exhibit critical behaviour that defies this description and is not well understood1. A paradigmatic example is the many-body localization (MBL) transition, which marks the breakdown of thermalization in an isolated quantum many-body system as its disorder increases beyond a critical value2-11. Characterizing quantum critical behaviour in an MBL system requires probing its entanglement over space and time4,5,7, which has proved experimentally challenging owing to stringent requirements on quantum state preparation and system isolation. Here we observe quantum critical behaviour at the MBL transition in a disordered Bose-Hubbard system and characterize its entanglement via its multi-point quantum correlations. We observe the emergence of strong correlations, accompanied by the onset of anomalous diffusive transport throughout the system, and verify their critical nature by measuring their dependence on the system size. The correlations extend to high orders in the quantum critical regime and appear to form via a sparse network of many-body resonances that spans the entire system12,13. Our results connect the macroscopic phenomenology of the transition to the system's microscopic structure of quantum correlations, and they provide an essential step towards understanding criticality and universality in non-equilibrium systems1,7,13.

From localized to delocalized plasmonic modes, first observation of superradiant scattering in disordered semi-continuous metal films

Our study proposes a new way to observe and explain the presence of extended plasmonic modes in disordered semi-continuous metal films before the percolation threshold. Attenuated total reflection spectroscopy allows us to follow the transition of plasmon modes from localized to delocalized resonances, but also reveals unobserved collective plasmon modes. These bright modes with out-of-plane polarization are transverse collective plasmonic resonances. By increasing the density of metallic nanoparticles in a wavelength scale, we observe an angular squeezing and spectral broadening of these modes. This behavior can be explained considering that transverse localized surface plasmon resonances of each nanoparticle, all resonant, interact in a collective and coherent way via a common confined light mode: the evanescent wave. These many-body resonances, which have never been clearly identified in such disordered semi-continuous metal films, can be described by analogy with atomic physics as superradiant modes. Our first simulations, using dyadic Green’s formalism, demonstrate the existence of this mode for a dense array of plasmonic systems. In this regime, the radiation rate of the superradiant mode increases with the number of tied dipoles. This explains the spectral broadening observed in our work and constitutes the first manifestation of superradiance mode in plasmonic random structure.

Spin Polarization through Floquet Resonances in a Driven Central Spin Model

Adiabatically varying the driving frequency of a periodically driven many-body quantum system can induce controlled transitions between resonant eigenstates of the time-averaged Hamiltonian, corresponding to adiabatic transitions in the Floquet spectrum and presenting a general tool in quantum many-body control. Using the central spin model as an application, we show how such controlled driving processes can lead to a polarization-based decoupling of the central spin from its decoherence-inducing environment at resonance. While it is generally impossible to obtain the exact Floquet Hamiltonian in driven interacting systems, we exploit the integrability of the central spin model to show how techniques from quantum quenches can be used to explicitly construct the Floquet Hamiltonian in a restricted many-body basis and model Floquet resonances.

Quantum simulators by design: Many-body physics in reconfigurable arrays of tunnel-coupled traps

We present a novel platform for the bottom-up construction of itinerant many-body systems: ultracold atoms transferred from a Bose-Einstein condensate into freely configurable arrays of micro-lens generated focused-beam dipole traps. This complements traditional optical lattices and gives a new quality to the field of two-dimensional quantum simulators. The ultimate control of topology, well depth, atom number, and interaction strength is matched by sufficient tunneling. We characterize the required light fields, derive the Bose-Hubbard parameters for several alkali species, investigate the loading procedures and heating mechanisms. To demonstrate the potential of this approach, we analyze coupled annular Josephson contacts exhibiting many-body resonances.

Heating and many-body resonances in a periodically driven two-band system

We study the dynamics and stability in a strongly interacting resonantly driven two-band model. Using exact numerical simulations, we find a stable regime at large driving frequencies where the time evolution is governed by a local Floquet Hamiltonian that is approximately conserved out to very long times. For slow driving, on the other hand, the system becomes unstable and heats up to infinite temperature. While thermalization is relatively fast in these two regimes (but to different "temperatures"), in the crossover between them we find slow nonthermalizing time evolution: temporal fluctuations become strong and temporal correlations long lived. Microscopically, we trace back the origin of this nonthermalizing time evolution to the properties of rare Floquet many-body resonances, whose proliferation at lower driving frequency removes the approximate energy conservation, and thus produces thermalization to infinite temperature.

Exact scattering eigenstates in double quantum-dot systems with an interdot Coulomb interaction

We study a double quantum-dot system which consists of two leads of noninteracting electrons and two quantum dots with an interdot Coulomb interaction. We assume spinless electrons and consider arbitrary complex values of all lead-dot couplings and an interdot coupling. We construct exact many-electron scattering eigenstates whose incident states are free-electronic plane waves in the leads. Due to the interaction, some of the incident plane waves are scattered to two-body and three-body bound states. The binding strength of the many-body bound states is affected by the arrangement of the two quantum dots, by which we observe an interplay of the Coulomb interaction and quantum interference. We can understand the many-body bound states in terms of many-body resonances.