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DOE OSTI2024

Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes

Studies of many-body non-Hermitian parity-time (PT)-symmetric quantum systems are attracting a lot of interest due to their relevance in research areas ranging from quantum optics and continuously monitored dynamics to Euclidean wormholes in quantum gravity and dissipative quantum chaos. While a symmetry classification of non-Hermitian systems leads to 38 universality classes, we show that, under certain conditions, PT-symmetric systems are grouped into 24 universality classes. We identify 14 of them in a coupled two-site Sachdev-Ye-Kitaev (SYK) model and confirm the classification by spectral analysis using exact diagonalization techniques. Intriguingly, in 4 of these 14 universality classes, AIII ν , BDI ν † , BDI + + ν , and CI − − ν , we identify a basis in which the SYK Hamiltonian has a block structure in which some blocks are rectangular, with ν ∈ N the difference between the number of rows and columns. We show analytically that this feature leads to the existence of ν robust purely eigenvalues, whose level statistics follow the predictions of Hermitian random matrix theory for classes A, AI, BDI, and CI, respectively. We have recently found that this ν is a topological invariant, so these classes are topological. By contrast, nontopological real eigenvalues display a crossover between Hermitian and non-Hermitian level statistics. Similarly to the case of Lindbladian dynamics, the reduction of universality classes leads to unexpected results, such as the absence of Kramers degeneracy in a given sector of the theory. Another novel feature of the classification scheme is that different sectors of the PT-symmetric Hamiltonian may have different symmetries. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2024

Lyapunov exponent as a signature of dissipative many-body quantum chaos

A distinct feature of Hermitian quantum chaotic dynamics is the exponential increase of certain out-of-time-order correlation (OTOC) functions around the Ehrenfest time with a rate given by a Lyapunov exponent. Physically, the OTOCs describe the growth of quantum uncertainty that crucially depends on the nature of the quantum motion. Here, we employ the OTOC in order to provide a precise definition of dissipative quantum chaos. For this purpose, we compute analytically the Lyapunov exponent for the vectorized formulation of the large- q limit of a q -body Sachdev-Ye-Kitaev model coupled to a Markovian bath. These analytic results are confirmed by an explicit numerical calculation of the Lyapunov exponent for several values of q ≥ 4 based on the solutions of the Schwinger-Dyson and Bethe-Salpeter equations. We show that the Lyapunov exponent decreases monotonically as the coupling to the bath increases and eventually becomes negative at a critical value of the coupling signaling a transition to a dynamics which is no longer quantum chaotic. Therefore, a positive Lyapunov exponent is a defining feature of dissipative many-body quantum chaos. The observation of the breaking of the exponential growth for sufficiently strong coupling suggests that dissipative quantum chaos may require in certain cases a sufficiently weak coupling to the environment. Published by the American Physical Society 2024

García-García, Antonio M.↗
DOE OSTI2020

Characterization of quantum chaos by two-point correlation functions

In this work, we propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair correlations between these operators can be organized into a matrix with a random-matrix-like spectrum. This approach is particularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Encoding an Oscillator into Many Oscillators

An outstanding challenge for quantum information processing using bosonic systems is Gaussian errors such as excitation loss and added thermal noise errors. Thus, bosonic quantum error correction is essential. Most bosonic quantum error correction schemes encode a finite-dimensional logical qubit or qudit into noisy bosonic oscillator modes. In this case, however, the infinite-dimensional bosonic nature of the physical system is lost at the error-corrected logical level. On the other hand, there are several proposals for encoding an oscillator mode into many noisy oscillator modes. However, these oscillator-into-oscillators encoding schemes are in the class of Gaussian quantum error correction. Therefore, these codes cannot correct practically relevant Gaussian errors due to the established no-go theorems that state that Gaussian errors cannot be corrected by using only Gaussian resources. Here, we circumvent these no-go results and show that it is possible to correct Gaussian errors by using Gottesman-Kitaev-Preskill (GKP) states as non-Gaussian resources. In particular, we propose a non-Gaussian oscillator-into-oscillators code, namely the GKP two-mode squeezing code, and demonstrate that it can quadratically suppress additive Gaussian noise errors in both the position and momentum quadratures except for a small sublogarithmic correction. Furthermore, we demonstrate that our GKP two-mode squeezing code is near optimal in the weak noise limit by proving via quantum information theoretic tools that quadratic noise suppression is optimal when we use two physical oscillator modes. Lastly, in this work we show that our non-Gaussian oscillator encoding scheme can also be used to correct excitation loss and thermal noise errors, which are dominant error sources in many realistic bosonic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Simulating exotic phases of matter with bond-directed interactions with arrays of Majorana-Cooper pair boxes

It is suggested that networks of Majorana-Cooper pair boxes connected by metallic nanowirescan simulate various exotic states of matter. In this simulations Majorana-Cooper boxes play therole of effective spins S=1/2 and the metallic connections generate the Kondo screening and theRuderman-Kittel-Kasuya-Yosida (RKKY) interaction. Depending on what prevails - whether it isthe Kondo effect or the RKKY exchange, one will have either an effective spin model or a Kondolattice. The list of exotic stets includes the famous hexagonal Kitaev model, a generalization of thismodel for a Kondo lattice and various spin models with three-spin interactions. A special emphasizeis made on the discussion of the Kondo lattice scenario.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Structural, electronic, and magnetic properties of nearly ideal J eff = 1/2 iridium halides

Heavy transition metal magnets with J e f f = 1 2 electronic ground states have attracted recent interest due to their penchant for hosting new classes of quantum spin liquids and superconductors. Unfortunately, model systems with ideal J e f f = 1 2 states are scarce due to the importance of noncubic local distortions in most candidate materials. In this work, we identify a family of iridium halide systems [i.e., K 2 Ir Cl 6 , K 2 Ir Br 6 , ( NH 4 ) 2 Ir Cl 6 , and Na 2 Ir Cl 6 · 6 ( H 2 O ) ] with Ir 4 + electronic ground states exhibiting extremely small deviations from the ideal J e f f = 1 2 limit. We also find ordered magnetic ground states for the three anhydrous systems, with single-crystal neutron diffraction on K 2 Ir Br 6 revealing type-I antiferromagnetism. This spin configuration is consistent with expectations for significant Kitaev exchange in a face-centered-cubic magnet. This work establishes that incorporating isolated Ir X 6 octahedra in materials, where X is a halogen ion with a low electronegativity, is an effective design principle for realizing unprecedented proximity to the pure J e f f = 1 2 state. However, at the same time, we highlight undeniable deviations from this ideal state, even in clean materials with ideal Ir X 6 octahedra as inferred from the global cubic crystal structures.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Integer versus half-integer spin on an approximate honeycomb lattice

Recent interest in honeycomb lattice materials has focused on their potential to host quantum spin liquid (QSL) states. Variations in bond angles and spin allow a range of interesting behaviors on this lattice, from the predicted QSL ground state of the Kitaev model to exotic magnetic orders. Here we report the physical properties of two compounds with rare earths on an approximate honeycomb lattice. Here, the isostructural compounds Nd 2 S 5 Sn (J = 9/2) and Pr 2 S 5 Sn (J = 4) permit a direct comparison of half-integer versus integer spins on this lattice. We find strikingly different magnetic properties for the two compounds. Nd 2 S 5 Sn orders antiferromagnetically at T N ≈ 2.5 K and undergoes several magnetic transitions to other ordered states under applied field. Pr 2 S 5 Sn displays no magnetic ordering transition above T = 0.41 K, and may be proximate to a spin liquid state.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Stacking disorder and thermal transport properties of α-RuCl 3

α-RuCl 3 , a well-known candidate material for Kitaev quantum spin liquid, is prone to stacking disorder due to the weak van der Waals bonding between the honeycomb layers. After a decade of intensive experimental and theoretical studies, the detailed correlation between stacking degree of freedom, structure transition, magnetic, and thermal transport properties remains unresolved. In this work, we reveal the effects of a small amount of stacking disorder inherent even in high quality α-RuCl 3 crystals. This small amount of stacking disorder results in the variation of the magnetic ordering temperature, and it suppresses the structure transition and thermal conductivity. Crystals with a minimal amount of stacking disorder have a T N > 7.4 K and exhibit a well-defined structure transition around 140 K upon cooling. For those with more stacking faults and a T N below 7 K, the structure transition occurs well below 140 K upon cooling and is incomplete, manifested by the diffuse streaks and the coexistence of both high-temperature and low-temperature phases down to the lowest measurement temperature. Both types of crystals exhibit oscillatory field-dependent thermal conductivity and a plateaulike feature in thermal Hall resistivity in the field-induced quantum spin liquid state. However, α-RuCl 3 crystals with a minimal amount of stacking disorder have a higher thermal conductivity that pushes the thermal Hall conductivity to be closer to the half-integer quantized value. Importantly, these findings demonstrate a strong correlation between layer stacking, structure transition, magnetic, and thermal transport properties, underscoring the importance of interlayer coupling in α-RuCl3 despite the weak van der Waals bonding.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Universal transport in periodically driven systems without long-lived quasiparticles

An intriguing regime of universal charge transport at high entropy density has been proposed for periodically driven interacting one-dimensional systems with Bloch bands separated by a large single-particle band gap. For weak interactions, a simple picture based on well-defined Floquet quasiparticles suggests that the system should host a quasisteady state current that depends only on the populations of the system's Floquet-Bloch bands and their associated quasienergy winding numbers. Here we show that such topological transport persists into the strongly interacting regime where the single-particle lifetime becomes shorter than the drive period. Analytically, we show that the value of the current is insensitive to interaction-induced band renormalizations and lifetime broadening when certain conditions are met by the system's nonequilibrium distribution function. We show that these conditions correspond to a quasisteady state. We support these predictions through numerical simulation of a system of strongly interacting fermions in a periodically modulated chain of Sachdev-Ye-Kitaev dots. Our paper establishes universal transport at high entropy density as a robust far from equilibrium topological phenomenon, which can be readily realized with cold atoms in optical lattices. Published by the American Physical Society 2024

Esin, Iliya (ORCID:0000000329590617)↗
DOE OSTI2024

Quantum chaos on edge

Recently, the physics of many-body quantum chaotic systems close to their ground states has come under intensified scrutiny. Such studies are motivated by the emergence of model systems exhibiting chaotic fluctuations throughout the entire spectrum [the Sachdev-Ye-Kitaev (SYK) model being a renowned representative] as well as by the physics of holographic principles, which likewise unfold close to ground states. Interpreting the edge of the spectrum as a quantum critical point, here we combine a wide range of analytical and numerical methods to the identification and comprehensive description of two different universality classes: the near edge physics of “sparse” and the near edge of “dense” chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension, which is exponentially small or algebraically small in the sparse and dense case, respectively. Notable representatives of the two classes are generic chaotic many-body models (sparse) and invariant random matrix ensembles or chaotic gravitational systems (dense). While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different. Considering the SYK model as a representative of the sparse class, we apply a combination of field theory and exact diagonalization to a detailed discussion of its edge spectrum. Conversely, Jackiw-Teitelboim gravity is our reference model for the dense class, where an analysis of the gravitational path integral and random matrix theory reveal universal differences to the sparse class, whose implications for the construction of holographic principles we discuss. Published by the American Physical Society 2024

Altland, Alexander (ORCID:0000000229914805)↗
DOE OSTI2025

Almost strong zero modes at finite temperature

Interacting fermionic chains exhibit extended regions of topological degeneracy of their ground states as a result of the presence of Majorana or parafermionic zero modes localized at the edges. In the opposite limit of infinite temperature, the corresponding nonintegrable spin chains, obtained via generalized Jordan-Wigner mapping, are known to host so-called almost strong zero modes, which are long-lived with respect to any bulk excitations. Here we study the fairly unexplored territory that bridges these two extreme cases of zero and infinite temperature. We blend two established techniques for states, the Lanczos series expansion and a tensor network ansatz, uplifting them to the level of operator algebra. This allows us to efficiently simulate large system sizes for arbitrarily long timescales and to extract the temperature-dependent decay rates. We observe that for the Kitaev-Hubbard model, the decay rate of the edge mode depends exponentially on the inverse temperature 𝛽, and on an effective energy scale Δ eff that is greater than the thermodynamic gap of the system Δ.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Passive Environment-Assisted Quantum Communication with GKP States

Bosonic pure-loss channel, which represents the process of photons decaying into a vacuum environment, has zero quantum capacity when the channel’s transmissivity is less than 50%. Modeled as a beam splitter interaction between the system and its environment, the performance of bosonic pure-loss channel can be enhanced by controlling the environment state. We show that by choosing the ideal Gottesman-Kitaev-Preskill (GKP) states for the system and its environment, perfect transmission of quantum information through a beam splitter is achievable at arbitrarily low transmissivities. Our explicit constructions allow for experimental demonstration of the improved performance of a quantum channel through passive environment assistance, which is potentially useful for quantum transduction where the environment state can be naturally controlled. In practice, it is crucial to consider finite-energy constraints, and high-fidelity quantum communication through a beam splitter remains achievable with GKP states at the few-photon level.

Wang, Zhaoyou [Univ. of Chicago, IL (United States↗
DOE OSTI2023

Qubit-Oscillator Concatenated Codes: Decoding Formalism and Code Comparison

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the errorcorrecting power of the original qubit codes. It is not clear how to concatenate optimally, given that there are several bosonic codes and concatenation schemes to choose from, including the recently discovered Gottesman-Kitaev-Preskill (GKP) – stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)] that allow protection of a logical bosonic mode from fluctuations of the conjugate variables of the mode. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog or Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing and formulate qudit versions of GKP-stabilizer codes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Sparsity dependence of Krylov state complexity in the SYK model

We study the Krylov state complexity of the Sachdev-Ye-Kitaev (SYK) model for 𝑁 ≤28 Majorana fermions with 𝑞-body fermion interaction with 𝑞 =4, 6, 8 for a range of sparse parameter 𝑘 that controls the number of remaining terms in the original SYK model after sparsification. The critical value of 𝑘 below which the model ceases to be holographic, denoted 𝑘 𝑐 , has been subject of several recent investigations. Using Krylov complexity as a probe, we find that the peak value of complexity does not change as we increase 𝑘 beyond 𝑘 ≥ 𝑘 min at large temperatures. We argue that this behavior is related to the change in the holographic nature of the Hamiltonian in the sparse SYK-type models such that the model is holographic for all 𝑘 ≥ 𝑘 min ≈ 𝑘 𝑐 . Our results provide a novel way to determine 𝑘 𝑐 in SYK-type models.

gauge-gravity dualitites↗
DOE OSTI2026

Evidence of Chiral Fermion Edge Modes through Geometric Engineering of Thermal Hall Effect in 𝛼−RuCl 3

The experimental observation of half-integer-quantized thermal Hall conductivity in the Kitaev candidate material α-RuCl 3 has served as a signature of non-Abelian anyons through an associated chiral Majorana edge mode. However, both the reproducibility of the quantized thermal Hall conductivity and the fundamental nature of the associated heat carriers, whether bosonic or fermionic, are subjects of ongoing and vigorous debate. In a recent theoretical work, it was proposed that varying the sample geometry through creating constrictions can distinguish between different origins of the thermal Hall effect in magnetic insulators. Here, in this study, we provide experimental evidence of chiral fermion edge modes by comparing the thermal Hall effect of a geometrically constricted α-RuCl 3 sample with that of an unconstricted sample. In contrast to the unconstricted crystals where the thermal Hall signal fades below 5 K, the constricted crystals display a significant thermal Hall signal that remains measurable even at 2 K. This sharp difference agrees well with the theoretical prediction and provides compelling evidence for the contribution of chiral fermion edge modes to the thermal Hall effect in α-RuCl 3 . More broadly, this work confirms that the geometry dependence of the thermal Hall effect can help identify chiral spin liquids in candidate materials like α-RuCl 3 and paves the way for the experimental realization of thermal anyon interferometry.

Zhang, Heda [Oak Ridge National Laboratory (ORNL),↗
DOE OSTI2022

Exotic invertible phases with higher-group symmetries

We investigate a family of invertible phases of matter with higher-dimensional exotic excitations in even spacetime dimensions, which includes and generalizes the Kitaev’s chain in 1+1d. The excitation has \mathbb{Z}_2 ℤ 2 higher-form symmetry that mixes with the spacetime Lorentz symmetry to form a higher group spacetime symmetry. We focus on the invertible exotic loop topological phase in 3+1d. This invertible phase is protected by the \mathbb{Z}_2 ℤ 2 one-form symmetry and the time-reversal symmetry, and has surface thermal Hall conductance not realized in conventional time-reversal symmetric ordinary bosonic systems without local fermion particles and the exotic loops. We describe a UV realization of the invertible exotic loop topological order using the SO(3)_- S O ( 3 ) − gauge theory with unit discrete theta parameter, which enjoys the same spacetime two-group symmetry. We discuss several applications including the analogue of ``fermionization’’ for ordinary bosonic theories with \mathbb{Z}_2 ℤ 2 non-anomalous internal higher-form symmetry and time-reversal symmetry.

Hsin, Po-Shen↗
DOE OSTI2023

Measurement-based quantum simulation of Abelian lattice gauge theories

Numerical simulation of lattice gauge theories is an indispensable tool in high energy physics, and their quantum simulation is expected to become a major application of quantum computers in the future. In this work, for an Abelian lattice gauge theory in d d spacetime dimensions, we define an entangled resource state (generalized cluster state) that reflects the spacetime structure of the gauge theory. We show that sequential single-qubit measurements with the bases adapted according to the former measurement outcomes induce a deterministic Hamiltonian quantum simulation of the gauge theory on the boundary. Our construction includes the (2+1) ( 2 + 1 ) -dimensional Abelian lattice gauge theory simulated on three-dimensional cluster state as an example, and generalizes to the simulation of Wegner’s lattice models M_{(d,n)} M ( d , n ) that involve higher-form Abelian gauge fields. We demonstrate that the generalized cluster state has a symmetry-protected topological order with respect to generalized global symmetries that are related to the symmetries of the simulated gauge theories on the boundary.Our procedure can be generalized to the simulation of Kitaev’s Majorana chain on a fermionic resource state. We also study the imaginary-time quantum simulation with two-qubit measurements and post-selections, and a classical-quantum correspondence, where the statistical partition function of the model M_{(d,n)} M ( d , n ) is written as the overlap between the product of two-qubit measurement bases and the wave function of the generalized cluster state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A symmetry algebra in double-scaled SYK

The double-scaled limit of the Sachdev-Ye-Kitaev (SYK) model takes the number of fermions and their interaction number to infinity in a coordinated way. In this limit, two entangled copies of the SYK model have a bulk description of sorts known as the “chord Hilbert space”. We analyze a symmetry algebra acting on this Hilbert space, generated by the two Hamiltonians together with a two-sided operator known as the chord number. This algebra is a deformation of the JT gravitational algebra, and it contains a subalgebra that is a deformation of the \mathfrak{sl}_2 𝔰 𝔩 2 near-horizon symmetries. The subalgebra has finite-dimensional unitary representations corresponding to matter moving around in a discrete Einstein-Rosen bridge. In a semiclassical limit the discreteness disappears and the subalgebra simplifies to \mathfrak{sl}_2 𝔰 𝔩 2 , but with a non-standard action on the boundary time coordinate. One can make the action of \mathfrak{sl}_2 𝔰 𝔩 2 algebra more standard at the cost of extending the boundary circle to include some “fake” portions. Such fake portions also accommodate certain subtle states that survive the semi-classical limit, despite oscillating on the scale of discreteness. We discuss applications of this algebra, including sub-maximal chaos, the traversable wormhole protocol, and a two-sided OPE.

97 MATHEMATICS AND COMPUTING↗