arXiv subjects

Stephen R. Clark

Publications and source records attributed to Stephen R. Clark.

At least 19 recordsLinked to original sources

arXiv2025

Accelerated calculation of impurity Green's functions exploiting the extreme Mpemba effect

Simulating the dynamics of quantum impurity models remains a fundamental challenge due to the complex memory effects that arise from system-environment interactions. Of particular interest are two-time correlation functions of an impurity, which are central to the characterization of these many-body systems, and are a cornerstone of the description of correlated materials in dynamical mean field theory (DMFT). In this work, we extend our previous work on the extrapolation of single-time observables to demonstrate an efficient scheme for computing two-time impurity correlation functions, by combining the non-Markovian quantum Mpemba effect (NMQMpE) with a dynamical map-based framework for open quantum systems. Our method is benchmarked against exact and known accurate results in prototypical impurity models for both fermionic and bosonic environments, demonstrating significant computational savings compared to state-of-the-art methods.

quant-ph↗

arXiv2024

Extracting Dynamical Maps of Non-Markovian Open Quantum Systems

The most general description of quantum evolution up to a time $\tau$ is a completely positive tracing preserving map known as a dynamical map $\hat{\Lambda}(\tau)$. Here we consider $\hat{\Lambda}(\tau)$ arising from suddenly coupling a system to one or more thermal baths with a strength that is neither weak nor strong. Given no clear separation of characteristic system/bath time scales $\hat{\Lambda}(\tau)$ is generically expected to be non-Markovian, however we do assume the ensuing dynamics has a unique steady state implying the baths possess a finite memory time $\tau_{\rm m}$. By combining several techniques within a tensor network framework we directly and accurately extract $\hat{\Lambda}(\tau)$ for a small number of interacting fermionic modes coupled to infinite non-interacting Fermi baths. We employ the Choi-Jamiolkowski isomorphism so that $\hat{\Lambda}(\tau)$ can be fully reconstructed from a single pure state calculation of the unitary dynamics of the system, bath and their replica auxillary modes up to time $\tau$. From $\hat{\Lambda}(\tau)$ we also compute the time local propagator $\hat{\mathcal{L}}(\tau)$. By examining the convergence with $\tau$ of the instantaneous fixed points of these objects we establish their respective memory times $\tau^{\Lambda}_{\rm m}$ and $\tau^{\mathcal{L}}_{\rm m}$. Beyond these times, the propagator $\hat{\mathcal{L}}(\tau)$ and dynamical map $\hat{\Lambda}(\tau)$ accurately describe all the subsequent long-time relaxation dynamics up to stationarity. Our numerical examples of interacting spinless Fermi chains and the single impurity Anderson model demonstrate regimes where our approach can offer a significant speedup in determining the stationary state compared to directly simulating the long-time limit.

quant-ph↗

arXiv2024

Entropy production in the mesoscopic-leads formulation of quantum thermodynamics

Understanding the entropy production of systems strongly coupled to thermal baths is a core problem of both quantum thermodynamics and mesoscopic physics. While there exist many techniques to accurately study entropy production in such systems, they typically require a microscopic description of the baths, which can become numerically intractable to study for large systems. Alternatively an open-systems approach can be employed with all the nuances associated with various levels of approximation. Recently, the mesoscopic leads approach has emerged as a powerful method for studying such quantum systems strongly coupled to multiple thermal baths. In this method, a set of discretised lead modes, each locally damped, provide a Markovian embedding. Here we show that this method proves extremely useful to describe entropy production of a strongly coupled open quantum system. We show numerically, for both non-interacting and interacting setups, that a system coupled to a single bath exhibits a thermal fixed point at the level of the embedding. This allows us to use various results from the thermodynamics of quantum dynamical semi-groups to infer the non-equilibrium thermodynamics of the strongly coupled, non-Markovian central systems. In particular, we show that the entropy production in the transient regime recovers the well established microscopic definitions of entropy production with a correction that can be computed explicitly for both the single- and multiple-lead cases.

quant-ph↗

arXiv2024

Dephasing-assisted transport in a tight-binding chain with a linear potential

An environment interacting with a quantum system can enhance transport through the suppression of quantum effects responsible for localization. In this paper, we study the interplay between bulk dephasing and a linear potential in a boundary-driven tight-binding chain. A linear potential induces Wannier-Stark localization in the absence of noise, while dephasing induces diffusive transport in the absence of a tilt. We derive an approximate expression for the steady-state current as a function of both dephasing and tilt which closely matches the exact solution for a wide range of parameters. From it, we find that the maximum current occurs for a dephasing rate equal to the period of Bloch oscillations in the Wannier-Stark localized system. We also find that the current displays a maximum as a function of the system size, provided that the total potential tilt across the chain remains constant. Our results can be verified in current experimental platforms and represents a step forward in analytical studies of environment-assisted transport.

cond-mat.stat-mech↗

arXiv2024

Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models

We develop a unified framework for open quantum systems composed of many mutually interacting quantum spins, or any isomorphic systems like qubits and qudits, surrounded by one or more independent bosonic baths. Our framework, based on Schwinger-Keldysh field theory (SKFT), can handle arbitrary spin value S, dimensionality of space, and geometry, while being applicable to a large parameter space for system and bath or their coupling. It can probe regimes in which non-Markovian dynamics and nonperturbative effects pose formidable challenges for other state-of-the-art theoretical methods. This is achieved by working with the two-particle irreducible (2PI) effective action, which resums classes of Feynman diagrams of SKFT to an infinite order. Furthermore, such diagrams are generated via an expansion in 1/N, where N is the number of Schwinger bosons we employ to map spin operators onto canonically commuting ones, rather than via conventional expansion in system-bath coupling constant. We carefully benchmark our SKFT+2PI-computed results vs. numerically (quasi)exact ones from tensor network calculations applied to the archetypical spin-boson model where both methodologies are applicable. Additionally, we demonstrate the capability of SKFT+2PI to handle a much more complex spin-chain-boson model with multiple baths interacting with each spin where no benchmark from other methods is available at present. The favorable numerical cost of solving integro-differential equations produced by the SKFT+2PI framework with an increasing number of spins and time steps makes it a promising route for simulating driven-dissipative systems in quantum computing, quantum magnonics, and quantum spintronics.

quant-ph↗

arXiv2024

Implementation of Firm-Dispatchable Generation in South Africa

South Africa is currently facing a critical situation in its power generation landscape, which is plagued by frequent power outages and the need to move from fossil fuels to renewable energy sources. This period emphasizes the importance of having firm-dispatchable power to balance out the intermittent nature of wind and solar energy sources. The paper proposes to repurpose old coal-fired power plants to generate firm-dispatchable energy in line with the principles of a Just Transition. Eskom's coal plants are approaching the end of their economic life, and their declining energy availability factor is becoming a challenge in meeting the country's energy needs. The study suggests that a comprehensive strategy that integrates wind, solar, and firm-dispatchable power can be cost-effective and reliable compared to the traditional coal-based approach or the nuclear alternative. The study emphasizes the necessity of a 25-year plan that would invest in flexible and modular dispatchable generation. It also highlights the strategic location of this generating capacity, including repurposing decommissioned coal plant sites. The proposed model integrates private investment, adheres to established best practices, and emphasizes adaptability to changing demand dynamics. The study provides a roadmap for enabling firm-dispatchable capacity for South Africa's energy transition, emphasizing economic prudence, environmental sustainability, and alignment with the principles of the Just Transition program.

eess.SY↗

arXiv2024

Firm-Dispatchable Power and its Requirement in a Power System based on Variable Generation

Many countries have commenced a transition from fossil fuel-based electricity generation systems to sustainable systems based on wind and solar generation. It is often noted that the least cost approach would involve a massive scale-up in the building of variable renewables, supported by battery storage and gas peaking plants. The required backup should be firm-dispatchable generation rather than peaking power. The wind and solar generation aspects for this system are clearly defined and understood, however, the term firm-dispatchable power is not defined and the specific requirements are poorly understood. This study seeks to define firm-dispatchable power in this context and its requirement in the sustainable generation system. The study compares 100% renewable generation scenarios from South Africa, Texas, and the UK to demonstrate the requirement for this firm-dispatchable generation. The results indicate that firm-dispatchable generation must be available to replace the renewable generation completely. The required installed capacity for this firm-dispatchable generation does not vary with the distinct demand profiles of the different locations or their comparative renewable generation profiles. It also does not change significantly with the use of energy storage. The usage for this firm-dispatchable generation will vary due to the comparative economics of its use, but the requirement for its installation does not change.

eess.SY↗

arXiv2024

Specialising Neural-network Quantum States for the Bose Hubbard Model

Projected variational wavefunctions such as the Gutzwiller, many-body correlator and Jastrow ansatzes have provided crucial insight into the nature of superfluid-Mott insulator transition in the Bose Hubbard model (BHM) in two or more spatial dimensions. However, these ansatzes have no obvious tractable and systematic way of being improved. A promising alternative is to use Neural-network quantum states (NQS) based on Restricted Boltzmann Machines (RBMs). With binary visible and hidden units NQS have proven to be a highly effective at describing quantum states of interacting spin-1/2 lattice systems. The application of NQS to bosonic systems has so far been based on one-hot encoding from machine learning where the multi-valued site occupation is distributed across several binary-valued visible units of an RBM. Compared to spin-1/2 systems one-hot encoding greatly increases the number of variational parameters whilst also making their physical interpretation opaque. Here we revisit the construction of NQS for bosonic systems by reformulating a one-hot encoded RBM into a correlation operator applied to a reference state, analogous to the structure of the projected variational ansatzes. In this form we then propose a number of specialisations of the RBM motivated by the physics of the BHM and the ability to capture exactly the projected variational ansatzes. We analyse in detail the variational performance of these new RBM variants for a 10 x 10 BHM, using both a standard Bose condensate state and a pre-optimised Jastrow + many-body correlator state as the reference state of the calculation. Several of our new ansatzes give robust results as nearly good as one-hot encoding across the regimes of the BHM, but at a substantially reduced cost. Such specialised NQS are thus primed tackle bosonic lattice problems beyond the accuracy of classic variational wavefunctions.

cond-mat.quant-gas↗

arXiv2024

Non-Markovian Quantum Mpemba effect

Since it's rediscovery in the twentieth century, the Mpemba effect, where a far-from-equilibrium state may relax faster than a state closer to equilibrium, has been extensively studied in classical systems and has recently received significant attention in quantum systems. Many theories explaining this counter-intuitive behavior in classical systems rely on memory effects. However, in quantum systems, the relation between the Mpemba effect and memory has remained unexplored. In this work, we consider a general non-Markovian open quantum setting and reveal new classes of quantum Mpemba effects, with no analog in Markovian quantum dynamics. Generically, open quantum dynamics possess a finite memory time and a unique steady state. Due to non-Markovian dynamics, even if the system is initialized in the steady state it can take a long time to relax back. We find other initial states that reach the steady state much faster. Most notably, we demonstrate that there can be an initial state in which the system reaches the steady state within the finite memory time itself, therefore giving the fastest possible relaxation to stationarity. We verify the effect for quantum dot systems coupled to electronic reservoirs in equilibrium and non-equilibrium setups at weak, intermediate and strong coupling, and both with and without interactions. Our work provides new insights into the rich physics underlying accelerated relaxation in quantum systems.

quant-ph↗

arXiv2024

Giant rectification in strongly-interacting driven tilted systems

Correlated quantum systems feature a wide range of nontrivial effects emerging from interactions between their constituting particles. In nonequilibrium scenarios, these manifest in phenomena such as many-body insulating states and anomalous scaling laws of currents of conserved quantities, crucial for applications in quantum circuit technologies. In this work we propose a giant rectification scheme based on the asymmetric interplay between strong particle interactions and a tilted potential, each of which induces an insulating state on their own. While for reverse bias both cooperate and induce a strengthened insulator with an exponentially suppressed current, for forward bias they compete generating conduction resonances; this leads to a rectification coefficient of many orders of magnitude. We uncover the mechanism underlying these resonances as enhanced coherences between energy eigenstates occurring at avoided crossings in the system's bulk energy spectrum. Furthermore, we demonstrate the complexity of the many-body nonequilibrium conducting state through the emergence of enhanced density matrix impurity and operator space entanglement entropy close to the resonances. Our proposal paves the way for implementing a perfect diode in currently-available electronic and quantum simulation platforms.

quant-ph↗

arXiv2022

Thermally Driven Polaron Transport in Conjugated Polymers

We present a hybrid quantum-classical simulation of charge-polaron transport in conjugated polymers. The charge, which couples to the angular rotations of the monomers, is modeled via the time-dependent Schrödinger equation, while the monomers are treated classically via the Ehrenfest equations of motion. In addition, the system is thermalized by assuming that the monomers are subject to Brownian fluctuations modeled by the Langevin equation. Charge coupling to the monomer rotations localizes the particle into a Landau polaron, while the thermal fluctuations of the monomers causes polaron dynamics. The emergent low-energy scale of the model is the polaron reorganization energy, $E_r$, and thus $T_r = E_r/k_B$ is a convenient scale for the low-temperature dynamics. We investigate two types of dynamics -- both relevant for temperatures $T < T_r$. In the lower temperature regime the system remains in the same quasidiabatic state, corresponding to activationless polaron diffusion as the polaron crawls stochastically along the chain. As the temperature is raised, however, there is a cross-over to an additional activated transfer process which corresponds to hopping between diabatic states. We show that these processes exhibit Landau-Zener type dynamics. We note that as our model is general, it equally applies to exciton-polaron (i.e., energy) transport in conjugated polymers, and to charge and exciton polaron transport in quasi one-dimensional molecular stacks.

cond-mat.stat-mech↗

arXiv2021

Compact Neural-network Quantum State representations of Jastrow and Stabilizer states

Neural-network quantum states (NQS) have become a powerful tool in many-body physics. Of the numerous possible architectures in which neural-networks can encode amplitudes of quantum states the simplicity of the Restricted Boltzmann Machine (RBM) has proven especially useful for both numerical and analytical studies. In particular devising exact NQS representations for important classes of states, like Jastrow and stabilizer states, has provided useful clues into the strengths and limitations of the RBM based NQS. However, current constructions for a system of $N$ spins generate NQS with $M \sim O(N^2)$ hidden units that are very sparsely connected. This makes them rather atypical NQS compared to those commonly generated by numerical optimisation. Here we focus on compact NQS, denoting NQS with a hidden unit density $α= M/N \leq 1$ but with system-extensive hidden-visible unit connectivity. By unifying Jastrow and stabilizer states we introduce a new exact representation that requires at most $M=N-1$ hidden units, illustrating how highly expressive $α\leq 1$ can be. Owing to their structural similarity to numerical NQS solutions our result provides useful insights and could pave the way for more families of quantum states to be represented exactly by compact NQS.

quant-ph↗

arXiv2021

Neural-network Quantum States for Spin-1 systems: spin-basis and parameterization effects on compactness of representations

Neural network quantum states (NQS) have been widely applied to spin-1/2 systems where they have proven to be highly effective. The application to systems with larger on-site dimension, such as spin-1 or bosonic systems, has been explored less and predominantly using spin-1/2 Restricted Boltzmann Machines (RBMs) with a one-hot/unary encoding. Here we propose a more direct generalisation of RBMs for spin-1 that retains the key properties of the standard spin-1/2 RBM, specifically trivial product states representations, labelling freedom for the visible variables and gauge equivalence to the tensor network formulation. To test this new approach we present variational Monte Carlo (VMC) calculations for the spin-1 antiferromagnetic Heisenberg (AFH) model and benchmark it against the one-hot/unary encoded RBM demonstrating that it achieves the same accuracy with substantially fewer variational parameters. Further to this we investigate how the hidden unit complexity of NQS depend on the local single-spin basis used. Exploiting the tensor network version of our RBM we construct an analytic NQS representation of the Affleck-Kennedy-Lieb-Tasaki (AKLT) state in the $xyz$ spin-1 basis using only $M = 2N$ hidden units, compared to $M \sim O(N^2)$ required in the $S^z$ basis. Additional VMC calculations provide strong evidence that the AKLT state in fact possesses an exact compact NQS representation in the $xyz$ basis with only $M=N$ hidden units. These insights help to further unravel how to most effectively adapt the NQS framework for more complex quantum systems.

quant-ph↗

arXiv2020

Investigation of the Non-equilibrium State of Strongly Correlated Materials by Complementary Ultrafast Spectroscopy Techniques

Photoinduced non-thermal phase transitions are new paradigms of exotic non-equilibrium physics of strongly correlated materials. An ultrashort optical pulse can drive the system to a new order through complex microscopic interactions that do not occur in the equilibrium state. Ultrafast spectroscopies are unique tools to reveal the underlying mechanisms of such transitions which lead to transient phases of matter. Yet, their individual specificities often do not provide an exhaustive picture of the physical problem. One effective solution to enhance their performance is the integration of different ultrafast techniques. This provides an opportunity to simultaneously probe physical phenomena from different perspectives whilst maintaining the same experimental conditions. In this context, we performed complementary experiments by combining time-resolved reflectivity and time and angle-resolved photoemission spectroscopy. We demonstrated the advantage of this combined approach by investigating the complex charge density wave (CDW) phase in 1$\it{T}$-TiSe$_{2}$. Specifically, we show the key role of lattice degrees of freedom to establish and stabilize the CDW in this material.

cond-mat.str-el↗

arXiv2020

Tensor-network method to simulate strongly interacting quantum thermal machines

We present a methodology to simulate the quantum thermodynamics of thermal machines which are built from an interacting working medium in contact with fermionic reservoirs at fixed temperature and chemical potential. Our method works at finite temperature, beyond linear response and weak system-reservoir coupling, and allows for non-quadratic interactions in the working medium. The method uses mesoscopic reservoirs, continuously damped towards thermal equilibrium, in order to represent continuum baths and a novel tensor network algorithm to simulate the steady-state thermodynamics. Using the example of a quantum-dot heat engine, we demonstrate that our technique replicates the well known Landauer-Büttiker theory for efficiency and power. We then go beyond the quadratic limit to demonstrate the capability of our method by simulating a three-site machine with non-quadratic interactions. Remarkably, we find that such interactions lead to power enhancement, without being detrimental to the efficiency. Furthermore, we demonstrate the capability of our method to tackle complex many-body systems by extracting the super-diffusive exponent for high-temperature transport in the isotropic Heisenberg model. Finally, we discuss transport in the gapless phase of the anisotropic Heisenberg model at finite temperature and its connection to charge conjugation-parity, going beyond the predictions of single-site boundary driving configurations.

cond-mat.str-el↗

arXiv2020

Parallel time-dependent variational principle algorithm for matrix product states

Combining the time-dependent variational principle (TDVP) algorithm with the parallelization scheme introduced by Stoudenmire and White for the density matrix renormalization group (DMRG), we present the first parallel matrix product state (MPS) algorithm capable of time evolving one-dimensional (1D) quantum lattice systems with long-range interactions. We benchmark the accuracy and performance of the algorithm by simulating quenches in the long-range Ising and XY models. We show that our code scales well up to 32 processes, with parallel efficiencies as high as 86%. Finally, we calculate the dynamical correlation function of a 201-site Heisenberg XXX spin chain with $1/r^2$ interactions, which is challenging to compute sequentially. These results pave the way for the application of tensor networks to increasingly complex many-body systems.

quant-ph↗

arXiv2019

Excitonic and lattice contributions to the charge density wave in 1T-TiSe$_2$ revealed by a phonon bottleneck

Understanding collective electronic states such as superconductivity and charge density waves is pivotal for fundamental science and applications. The layered transition metal dichalcogenide 1T-TiSe2 hosts a unique charge density wave (CDW) phase transition whose origins are still not fully understood. Here, we present ultrafast time- and angle-resolved photoemission spectroscopy (TR-ARPES) measurements complemented by time-resolved reflectivity (TRR) which allows us to establish the contribution of excitonic and electron-phonon interactions to the CDW. We monitor the energy shift of the valence band (VB) and coupling to coherent phonons as a function of laser fluence. The VB shift, directly related to the CDW gap closure, exhibits a markedly slower recovery dynamics at fluences above Fth = 60 microJ cm-2. This observation coincides with a shift in the relative weight of coherently coupled phonons to higher frequency modes in time-resolved reflectivity (TRR), suggesting a phonon bottleneck. Using a rate equation model, the emergence of a high-fluence bottleneck is attributed to an abrupt reduction in coupled phonon damping and an increase in exciton dissociation rate linked to the loss of CDW superlattice phonons. Thus, our work establishes the important role of both excitonic and phononic interactions in the CDW phase transition and the advantage of combining complementary femtosecond techniques to understand the complex interactions in quantum materials.

cond-mat.str-el↗

arXiv2019

Thermodynamics of precision in quantum non equilibrium steady states

Autonomous engines operating at the nano-scale can be prone to deleterious fluctuations in the heat and particle currents which increase, for fixed power output, the more reversible the operation regime is. This fundamental trade-off between current fluctuations and entropy production forms the basis of the recently formulated thermodynamic uncertainty relations (TURs). However, these relations have so far only been derived for classical Markovian systems and can be violated in the quantum regime. In this paper we show that the geometry of quantum non-equilibrium steady-states alone, already directly implies the existence of a TUR, but with a looser bound. The geometrical nature of this result makes it extremely general, establishing a fundamental limit for the thermodynamics of precision. Our proof is based on the McLennan-Zubarev ensemble, which provides an exact description of non-equilibrium steady-states. We first prove that the entropy production of this ensemble can be expressed as a quantum relative entropy. The TURs are then shown to be a direct consequence of the quantum Cramer-Rao bound, a fundamental result from parameter estimation theory. By combining techniques from many-body physics and information sciences, our approach also helps to shed light on the delicate relationship between quantum effects and current fluctuations in autonomous machines.

cond-mat.stat-mech↗