We provide a comprehensive theory of magnetic phases in two-dimensional triangulene crystals, using both Hubbard model and density functional theory (DFT) calculations. We consider centrosymmetric and noncentrosymmetric triangulene crystals. In all cases DFT and the mean-field Hubbard model predict the emergence of broken-symmetry antiferromagnetic (ferrimagnetic) phases for the centrosymmetric (noncentrosymmetric) crystals. This includes the special case of the [4,4]triangulene crystal, whose noninteracting energy bands feature a gap with flat valence and conduction bands. We show how the lack of contrast between the local density of states of these bands, recently measured via scanning tunneling spectroscopy, is a natural consequence of a broken-symmetry Néel state that blocks intermolecular hybridization. Using random phase approximation, we also compute the spin wave spectrum of these crystals, including the recently synthesized [4,4]triangulene crystal. The results are in excellent agreement with the predictions of a Heisenberg spin model derived from multiconfiguration calculations for the unit cell. We conclude that experimental results are compatible with an antiferromagnetically ordered phase where each triangulene retains the spin predicted for the isolated species.

The relaxation dynamics of an open quantum system is determined by the competition between the coherent Hamiltonian dynamics of a system and the dissipative dynamics due to interactions with environments. It is therefore of fundamental interest to understand the transition from the coherent to incoherent regimes. We find that hitherto unrecognized quasiparticles—incoherentons—describe this coherent-to-incoherent transition in eigenmodes of a Liouvillian superoperator that governs the dynamics of an open quantum many-body system. Here, an incoherenton is defined as an interchain bound state in an auxiliary ladder system that represents the density matrix of a system. The Liouvillian eigenmodes are classified into groups with different decay rates that reflect the number of incoherentons involved therein. We also introduce a spectral gap—quantum coherence gap—that separates the different groups of eigenmodes. We demonstrate the existence of incoherentons in a lattice boson model subject to dephasing, and show that the quantum coherence gap closes when incoherentons are deconfined, which signals a dynamical transition from incoherent relaxation with exponential decay to coherent oscillatory relaxation. Furthermore, we discuss how the decoherence dynamics of quantum many-body systems can be understood in terms of the generation, localization, and diffusion of incoherentons.

I describe a concrete and efficient real-space renormalization approach that provides a unifying perspective on interface states in a wide class of Hermitian and non-Hermitian models, irrespective of whether they obey a traditional bulk-boundary principle or not. The emerging interface physics are governed by a flow of microscopic interface parameters, and the properties of interface states become linked to the fixed-point topology of this flow. In particular, the quantization condition of interface states converts identically into the question of the convergence to unstable fixed points. As its key merit, the approach can be directly applied to concrete models and utilized to design interfaces that induce states with desired properties, such as states with a predetermined and possibly symmetry-breaking energy. I develop the approach in general, and then demonstrate these features in various settings, including for the design of circular, triangular, and square-shaped complex dispersion bands and associated arcs at the edge of a two-dimensional system. Furthermore, I describe how this approach transfers to nonlinear settings, and demonstrate the efficiency, practicability, and consistency of this extension for a paradigmatic model of topological mode selection by distributed saturable gain and loss.

The influence of a magnetic field applied perpendicularly to the plane of a quasi two-dimensional, low-density classical Coulomb gas, with interparticle potential $U\left(r\right)\sim 1/r$, is studied using momentum-conserving dissipative particle dynamics simulations. The self-diffusion and structure of the gas are studied as functions of temperature and strength of the magnetic field. It is found that the gas undergoes a topological phase transition when the temperature is varied with, in accord with the Bohr–van Leeuwen (BvL) theorem, the structural properties being unaffected, resembling those of the strictly two-dimensional Kosterlitz-Thouless transition, with $U\left(r\right)\sim ln\left(r\right)$. Consistent with the BvL theorem, the transition temperature and the melting process of the condensed phase are unchanged by the field. Conversely, the self-diffusion coefficient of the gas is strongly reduced by the magnetic field. At the largest values of the cyclotron frequency, the self-diffusion coefficient is inversely proportional to the applied magnetic field. The implications of these results are discussed.

How adaptive evolution to one environmental stress improves or suppresses adaptation to another is an important problem in evolutionary biology. For instance, in microbiology, the change of resistance to one antibiotic by resistance acquisition by another drug is a critical issue that has been investigated as cross-resistance. Recent experiments on bacteria have suggested that the cross-resistance of their evolution to various stressful environments can be predicted based on the transcriptome changes after evolution under the corresponding stresses. However, there are no studies so far that explain a possible theoretical relationship between cross-resistance and changes in the transcriptome, which causes high-dimensional changes to cell phenotype. In the present paper, we show that a correlation exists between fitness change in stress tolerance evolution and response to the environment, using a cellular model with a high-dimensional phenotype and establishing the relationship theoretically by formulating a macroscopic potential theory against environmental and genetic changes. Finally, we applied the theory to experimental data on bacterial evolution under antibiotics, which demonstrates the theoretically predicted correlation between the fitness changes by evolution and transcriptome changes upon environmental stresses. Thus, evolution is predicted from transcriptome information in response to stresses before evolution.

In neural information processing, inputs modulate neural dynamics to generate desired outputs. To unravel the dynamics and underlying neural connectivity enabling such input-output association, we propose an exactly solvable neural-network model with a connectivity matrix explicitly consisting of inputs and required outputs. An analytic form of the response under the input is derived, while three distinctive types of responses including chaotic dynamics are obtained as distinctive bifurcations against input strength, depending on the neural sensitivity and number of inputs. Optimal performance is achieved at the onset of chaos. The relevance of the results to cognitive dynamics is discussed.

Pricing financial derivatives, in particular European-style options at different time-maturities and strikes, means a relevant problem in finance. The dynamics describing the price of vanilla options when constant volatilities and interest rates are assumed is governed by the Black-Scholes model, a linear parabolic partial differential equation with terminal value given by the payoff of the option contract and no additional boundary conditions. Here, we present a digital quantum algorithm to solve the Black-Scholes equation on a quantum computer by mapping it to the Schrödinger equation. The non-Hermitian nature of the resulting Hamiltonian is solved by embedding its propagator into an enlarged Hilbert space by using only one additional ancillary qubit. Moreover, due to the choice of periodic boundary conditions, given by the definition of the discretized momentum operator, we duplicate the initial condition, which substantially improves the stability and performance of the protocol. The algorithm shows a feasible approach for using efficient Hamiltonian simulation techniques as quantum signal processing to solve the price dynamics of financial derivatives on a digital quantum computer. Our approach differs from those based on Monte Carlo integration, exclusively focused on sampling the solution assuming the dynamics is known. We report expected accuracy levels comparable to classical numerical algorithms by using nine qubits to simulate its dynamics on a fault-tolerant quantum computer, and an expected success probability of the post-selection procedure due to the embedding protocol above 60%.

Recently, the physics of $J=3/2$ electrons on a honeycomb lattice has received attention with the suggestion of hosting an SU(8) Dirac semimetallic state. Motivated by this, in this work we provide a systematic study of the interplay of various hopping pathways and atomic spin-orbit coupling for the low-energy electrons in candidate $d^1$ transition-metal halides $M{X}_3$ $(M=\mathrm{Ti},\mathrm{Zr},\mathrm{Hf}; X=\mathrm{F},\mathrm{Cl},\mathrm{Br})$. By combining first-principles calculations and a minimal hopping Hamiltonian, we uncover the role of dominant direct metal-metal hopping on top of indirect metal-halide-metal hopping. This sets up a hierarchy of hopping pathways that centrally modify the SU(8) picture for the above materials. These hopping interactions, along with the spin-orbit coupling, lead to a plethora of exactly compensated metals instead of the SU(8) Dirac semimetal. Remarkably, the same can be understood as descendants of a topological insulator obtained by gapping out the SU(8) Dirac semimetallic phase. The resultant compensated metals have varied Fermi surface topology and are separated by Lifshitz phase transitions. We discuss the implications of the proximate Lifshitz transition, which may be accessed via strain, in the context of the relevant materials.

In cluster tomography, we propose measuring the number of clusters $N$ intersected by a line segment of length $\ell$ across a finite sample. As expected, the leading order of $N\left(\ell \right)$ scales as $a\ell$, where $a$ depends on microscopic details of the system. However, at criticality, there is often an additional nonlinearity of the form $bln\left(\ell \right)$, originating from the endpoints of the line segment. By performing large scale Monte Carlo simulations of both two- and three-dimensional percolation, we find that $b$ is universal and depends only on the angles encountered at the endpoints of the line segment intersecting the sample. Our findings are further supported by analytic arguments in two dimensions, building on results in conformal field theory. Being broadly applicable, cluster tomography can be an efficient tool for detecting phase transitions and characterizing the corresponding universality class in classical or quantum systems with a relevant cluster structure.

The variational quantum eigensolver (VQE) is regarded as a promising candidate of hybrid quantum-classical algorithms for near-term quantum computers. Meanwhile, VQE is confronted with a challenge that statistical error associated with measurement as well as systematic error could significantly hamper the optimization. To circumvent this issue, we propose the classically optimized VQE (CO-VQE), where the whole process of optimization is efficiently conducted on a classical computer. The efficacy of the method is guaranteed by the observation that quantum circuits with up to logarithmic depth are classically tractable via simulations of local subsystems with up to quasipolynomial cost (polynomial for constant depth). In CO-VQE, we only use quantum computers to measure nonlocal quantities after the parameters are optimized. As a proof of concept, we present numerical experiments on quantum spin models with topological phases. After the optimization, we identify the topological phases by nonlocal order parameters as well as unsupervised machine learning on inner products between quantum states. The proposed method maximizes the advantage of using quantum computers while avoiding strenuous optimization on noisy quantum devices. In addition, our paper indicates that clustering technique combined with the fidelity measured on quantum computers could be useful for phase classification in condensed-matter physics.

During the noisy intermediate-scale quantum (NISQ) era, quantum computational approaches refined to overcome the challenge of limited quantum resources are highly valuable. A comprehensive benchmark for a quantum computational approach in this spirit could provide insights toward further improvements. On the other hand, the accuracy of the molecular properties predicted by most of the quantum computations nowadays is still far off (not within chemical accuracy) compared to their corresponding experimental data. In this work, we propose a promising qubit-efficient quantum computational approach and present a comprehensive investigation by benchmarking quantum computation of the harmonic vibrational frequencies of a large set of neutral closed-shell diatomic molecules with results in great agreement with their experimental data. To this end, we construct the accurate Hamiltonian using molecular orbitals, derived from density functional theory to account for the electron correlation and expanded in the Daubechies wavelet basis set to allow an accurate representation in real space grid points, where an optimized compact active space is further selected so that only a reduced small number of qubits is sufficient to yield an accurate result. Typically, calculations achieved with 2 to 12 qubits using our approach would need 20 to 60 qubits using a traditional cc-pVDZ basis set with frozen core approximation to achieve similar accuracy. To justify the approach, we benchmark the performance of the Hamiltonians spanned by the selected molecular orbitals by first transforming the molecular Hamiltonians into qubit Hamiltonians and then using the exact diagonalization method to calculate the results, regarded as the best results achievable by quantum computation to compare to the experimental data. Furthermore, using the variational quantum eigensolver algorithm with the constructed qubit Hamiltonians, we show that the variational quantum circuit with the chemistry-inspired UCCSD ansatz can achieve the same accuracy as the exact diagonalization method except for systems whose Mayer bond order indices are larger than 2. For those systems, we then demonstrate that the heuristic hardware-efficient RealAmplitudes ansatz, even with a substantially shorter circuit depth, can provide a significant improvement over the UCCSD ansatz, verifying that the harmonic vibrational frequencies could be calculated accurately by quantum computation in the NISQ era.

We construct a class of exact eigenstates of the Hamiltonian obtained by projecting the Hubbard interaction term onto the flat band subspace of a generic lattice model. These exact eigenstates are many-body states in which an arbitrary number of localized fermionic particles coexist with a sea of mobile Cooper pairs with zero momentum. By considering the dice lattice as an example, we provide evidence that these exact eigenstates are, in fact, a manifestation of local integrals of motions of the projected Hamiltonian. In particular, the spin and particle densities retain memory of the initial state for a very long time if localized unpaired particles are present at the beginning of the time evolution. This shows that many-body localization of quasiparticles and superfluidity can coexist even in generic two-dimensional lattice models with flat bands, for which it is not known how to construct local conserved quantities. Our results open interesting perspectives on the old condensed-matter problem of the interplay between superconductivity and localization.

Twisted bilayer graphene is an exciting platform for exploring correlated quantum phases, extremely tunable with respect to both the single-particle bands and the interaction profile of electrons. Here, we investigate the phase diagram of twisted bilayer graphene as described by an extended Hubbard model on the honeycomb lattice with two fermionic orbitals (valleys) per site. Besides the special extended cluster interaction $Q$, we incorporate the effect of gating through an on-site Hubbard-interaction $U$. Within quantum Monte Carlo, we find valence-bond solid, Nel-valley antiferromagnetic or charge-density wave phases. Further, we elucidate the competition of these phases by noticing that the cluster interaction induces an exotic constraint on the Hilbert space, which we dub the cluster rule, in analogy to the famous pyrochlore spin-ice rule. Formulating the perturbative Hamiltonian by projecting into the cluster-rule manifold, we perform exact diagonalization and construct the fixed-point states of the observed phases. Finally, we compute the local electron density patterns as signatures distinguishing these phases, which could be observed with scanning tunneling microscopy. Our paper capitalizes on the notion of cluster constraints in the extended Hubbard model of twisted bilayer graphene and suggests a scheme towards realization of several symmetry-breaking insulating phases in a twisted-bilayer graphene sheet.

We use a recently derived gauge-invariant formulation of the problem of a two-level system coupled to an optical cavity to explore the transition between the weak and the ultrastrong coupling regimes of light-matter interaction. We explore this transition using the intensity correlations $g^{\left(2\right)}\left(\tau \right)$ of the emitted light, and we find strong, unbounded bunching of the emission from systems governed by the Rabi Hamiltonian. Surprisingly, this effect is observed not only in the ultrastrong coupling regime, but also for weakly coupled systems, where the Jaynes-Cummings Hamiltonian would predict the opposite, antibunched emission. This suggests that the higher-order correlations are a particularly sensitive probe of the divergence between the Jaynes-Cummings and Rabi Hamiltonians, and they can serve as an indicator of the breakdown of the rotating wave approximation. Our findings indicate also that the boundary between the weakly, strongly, and ultra-strongly-coupled dynamics is much richer than currently accepted.

Graphene quantum dots are promising candidates for qubits due to weak spin-orbit and hyperfine interactions. The hyperfine interaction, controllable via isotopic purification, could be the key to further improving the coherence. Here, we use isotopically enriched graphite crystals of both ${}^{12}\mathrm{C}$ and ${}^{13}\mathrm{C}$ grown by a high-pressure-high-temperature method to exfoliate graphene layers. We fabricated Hall bar devices and performed quantum transport measurements, revealing mobilities exceeding ${10}^5{\text{cm}}^2/\text{V}\text{s}$ and a long mean free path of microns, which are as high as natural graphene. Shubnikov–de Haas oscillations, quantum Hall effect up to the filling factor of one, and Brown-Zak oscillations due to the alignment of hBN and graphene are observed thanks to the high mobility. These results constitute a material platform for physics and engineering of isotopically enriched graphene qubits.

We present a novel method for simulating the noisy behavior of quantum computers, which allows to efficiently incorporate environmental effects in the driven evolution implementing the gates acting on the qubits. We show how to modify the noiseless gate executed by the computer to include any Markovian noise, hence resulting in what we will call a noisy gate. We compare our method with the IBM qiskit simulator, and show that it follows more closely both the analytical solution of the Lindblad equation as well as the behavior of a real quantum computer, where we ran algorithms involving up to 18 qubits; as such, our protocol offers a more accurate simulator for NISQ devices. The method is flexible enough to potentially describe any noise, including non-Markovian ones. The noise simulator based on this work is available as a python package at the link, https://pypi.org/project/quantum-gates.