Out-of-equilibrium dynamics of one-dimensional integrable quantum systems

Dinamica di fuori equilibrio di sistemi quantistici integrabili unidimensional

Non-equilibrium effects on charge and energy partitioning after an interaction quench

Charge and energy fractionalization are among the most intriguing features of interacting onedimensional fermion systems. In this work we determine how these phenomena are modified in the presence of an interaction quench. Charge and energy are injected into the system suddenly after the quench, by means of tunneling processes with a non-interacting one-dimensional probe. Here, we demonstrate that the system settles to a steady state in which the charge fractionalization ratio is unaffected by the pre-quenched parameters. On the contrary, due to the post-quench nonequilibrium spectral function, the energy partitioning ratio is strongly modified, reaching values larger than one. This is a peculiar feature of the non-equilibrium dynamics of the quench process and it is in sharp contrast with the non-quenched case, where the ratio is bounded by one.Comment: 12 pages, 4 figure

Quench-induced entanglement and relaxation dynamics in Luttinger liquids

We investigate the time evolution towards the asymptotic steady state of a one-dimensional interacting system after a quantum quench. We show that at finite times the latter induces entanglement between right- and left-moving density excitations, encoded in their cross-correlators, which vanishes in the long-time limit. This behavior results in a universal time decay ∝t−2 of the system spectral properties, in addition to nonuniversal power-law contributions typical of Luttinger liquids. Importantly, we argue that the presence of quench-induced entanglement clearly emerges in transport properties, such as charge and energy currents injected in the system from a biased probe and determines their long-time dynamics. In particular, the energy fractionalization phenomenon turns out to be a promising platform to observe the universal power-law decay ∝t−2 induced by entanglement and represents a novel way to study the corresponding relaxation mechanism

Transport Properties as a Tool to Study Universal Quench-induced Dynamics in 1D Systems

The study of the relaxation process that follows a quantum quench in 1D systems still represents an open research field. Here we consider a sudden change of the interparticle interaction and we identify a peculiar correlator of the system whose behavior is directly and deeply affected by the quench-induced dynamics. Interestingly, it features a universal power-law decay in time. Unfortunately, such a universal decay, although present, turns out to be subleading in intrinsic properties of the system such as the non- equilibrium spectral function. We thus consider a tunnel coupling of the system with a biased tip in order to be able to study also transport properties, namely the charge and energy current flowing from the tip to the system after the quench. In these quantities the universal power-law emerges clearly, especially if one focuses on energy current and its fractionalization into a right- and left- moving components. In particular, we show that the presence of a transient in the energy fractionalization ratio is a direct hallmark of the quench-induced relaxation. Within the setup we have considered, time-dependent transport properties are thus promoted to useful and promising tools to access the mechanisms at the base of the out-of- equilibrium dynamics following quantum quench

Asymmetries in the spectral density of an interaction-quenched Luttinger liquid

The spectral density of an interaction-quenched one-dimensional system is investigated. Both direct and inverse quench protocols are considered and it is found that the former leads to stronger effects on the spectral density with respect to the latter. Such asymmetry is directly reflected on transport properties of the system, namely the charge and energy current flowing to the system from a tunnel coupled biased probe. In particular, the injection of particles from the probe to the right-moving channel of the system is considered. The resulting fractionalization phenomena are strongly affected by the quench protocol and display asymmetries in the case of direct and inverse quench. Transport properties therefore emerge as natural probes for the observation of this quench-induced behavior

Universal scaling of quench-induced correlations in a one-dimensional channel at finite temperature

It has been shown that a quantum quench of interactions in a one-dimensional fermion system at zero temperature induces a universal power law $\propto t^{-2}$ in its long-time dynamics. In this paper we demonstrate that this behaviour is robust even in the presence of thermal effects. The system is initially prepared in a thermal state, then at a given time the bath is disconnected and the interaction strength is suddenly quenched. The corresponding effects on the long times dynamics of the non-equilibrium fermionic spectral function are considered. We show that the non-universal power laws, present at zero temperature, acquire an exponential decay due to thermal effects and are washed out at long times, while the universal behaviour $\propto t^{-2}$ is always present. To verify our findings, we argue that these features are also visible in transport properties at finite temperature. The long-time dynamics of the current injected from a biased probe exhibits the same universal power law relaxation, in sharp contrast with the non-quenched case which features a fast exponential decay of the current towards its steady value, and thus represents a fingerprint of quench-induced dynamics. Finally, we show that a proper tuning of the probe temperature, compared to that of the one-dimensional channel, can enhance the visibility of the universal power-law behaviour

Towards near-term quantum simulation of materials

Overview of data provided in support of Towards near-term quantum simulation of materials Contents of this folder: `analyse_materials_results.py`: script used to generate the summary tables and figures presented in the manuscript. `towards_quantum_simulation_data`: raw data used and produced when studying various 3D materials. `towards_quantum_simulation_analysis`: tables (in `.tex` format) and figures (as PDFs) presented in the manuscript. The contents of `towards_quantum_simulation_analysis` were generated by `analyse_materials_results.py`, i.e. the user need not run the script to produce the output files. Users can generate these analyses directly by running ```python analyse_materials_results.py```, though note the following packages will first need to be installed: `pandas >= 1.2.3` `numpy >= 1.23` `seaborn >= 0.11.1` `lfig >= 0.1.3` `matplotlib > 3.7.0` Included data Within `towards_quantum_simulation_data`, there are subfolders for each of the materials described in the manuscript, i.e. `SrVO3`, `GaAs`, `H3S`, `Si`, `Li2CuO2`. Within each material's folder are further subfolders for the `hamiltonian` and `encoding` used to represent the material, as well as subfolders for each of the `algorithms` studied. `hamiltonian`: files which specify the Hamiltonian for the material under study. There are a number of files `interactions.json` Hamiltonian terms in terms of Majorana monomials. `map_majorana_to_mode.json` keys are Majorana indices; values are the mode index to which they are associated. `map_mode_to_group.json` keys are mode indices; values are the group (or site) index to which they are associated. `map_group_to_position.json` keys are group indices; values are the corresponding 3D Cartesian coordinates of the lattice used to represent the material. `stage_data.json` contains key/value pairs of any other fields of interest. `encoding` files which specify the fermionic encoding which is customised for the material under study. `encoding.json` which details the edges of the hybrid compact encoding described in Section VI of the supplementary material. `precompiler.json` contains all the information which permits the encoding construction, including the Hamiltonian terms (`_interactions`) which match those in `hamiltonian/interactions.json`. The same mappings as present in the Hamiltonian data(a.g. `map_group_to_position`). `stage_data.json` contains key/value pairs of any other fields of interest. `algorithms` contains subfolders for each of the algorithms desribed in the manuscript Those explored for circuits depths: `TDSSplitTermsPriorityCircuitDepth` (TDS in the manuscript) `TDSSplitTermsPriorityCircuitDepthNoSwapNetwork` (TDS\*) `VQESplitTerms` (VQE) `VQESplitTermsNoSwapNetwork` (VQE*) each of which contain the files, inside the `circuitry` folder: `circuit_terms.csv`, which lists each individual term, together with their Pauli string and rotation angle, required to construct the corresponding quantum circuit `circuit_layers_to_implement.csv` groups the same terms into layers to achieve parallelism in the circuit. `stage_data.json` contains key/value pairs of any other fields of interest. and those used to compose measurement layers, as outlined in Section VII D of the supplementary material: `MeasurementCommutativity` `MeasurementNaiveQubitwise` `MeasurementNonCrossing` each of which contain the files, inside the `compilation` folder: `layers.csv` lists the terms which may be measured simultaneously to achieve the measurement strategies shown in Table S14. `stage_data.json` contains key/value pairs of any other fields of interest. CSV files In `towards_quantum_simulation_data`, there are unified CSV files containing the results of applying the procedures described in the manuscript to the target materials. `circuit_costs.csv`: results of running the circuit compiler described in the manuscript. `measurements.csv`: results of running the measurement compiler described in the manuscript. These CSVs are used in the analysis script `analyse_materials_results.py` to produce the figures and tables presented in the manuscript