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arXiv:2204.06817 · Quantum Science and Technology

Boundary-induced singularity in strongly-correlated quantum systems at finite temperature

Ding-Zu Wang, Guo‐Feng Zhang, Maciej Lewenstein, Shi-Ju Ran

Published Oct 16, 2023• 1 citation
arXivHTMLPDF

Abstract

Abstract Exploring the bulk-boundary correspondences and the boundary-induced phenomena in the strongly-correlated quantum systems belongs to the most fundamental topics of condensed matter physics. In this work, we study the bulk-boundary competition in a simulative Hamiltonian, with which the thermodynamic properties of the infinite-size translationally-invariant system can be optimally mimicked. The simulative Hamiltonian is constructed by introducing local interactions on the boundaries, coined as the entanglement-bath Hamiltonian (EBH) that is analogous to the heat bath. The terms within the EBH are variationally determined by a thermal tensor network method, with coefficients varying with the temperature of the infinite-size system. By treating the temperature as an adjustable hyper-parameter of the EBH, we identify a discontinuity point of the coefficients, dubbed as the ‘boundary quench point’ (BQP), whose physical implication is to distinguish the point, below which the thermal fluctuations from the boundaries to the bulk become insignificant. Fruitful phenomena are revealed when considering the simulative Hamiltonian, with the EBH featuring its own hyper-parameter, under the canonical ensembles at different temperatures. Specifically, a discontinuity in bulk entropy at the BQP is observed. The exotic entropic distribution, the relations between the symmetries of Hamiltonian and BQP, and the impacts from the entanglement-bath dimension are also explored. Our results show that such a singularity differs from those in the conventional thermodynamic phase transition points that normally fall into the Landau–Ginzburg paradigm. Our work provides the opportunities on exploring the exotic phenomena induced by the competition between the bulk and boundaries.

DOI
10.1088/2058-9565/ad038a

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Abstract Exploring the bulk-boundary correspondences and the boundary-induced phenomena in the strongly-correlated quantum systems belongs to the most fundamental topics of condensed matter physics. In this work, we study the bulk-boundary competition in a simulative Hamiltonian, with which the thermodynamic properties of the infinite-size translationally-invariant system can be optimally mimicked. The simulative Hamiltonian is constructed by introducing local interactions on the boundaries, coined as the entanglement-bath Hamiltonian (EBH) that is analogous to the heat bath. The terms within the EBH are variationally determined by a thermal tensor network method, with coefficients varying with the temperature of the infinite-size system. By treating the temperature as an adjustable hyper-parameter of the EBH, we identify a discontinuity point of the coefficients, dubbed as the ‘boundary quench point’ (BQP), whose physical implication is to distinguish the point, below which the thermal fluctuations from the boundaries to the bulk become insignificant. Fruitful phenomena are revealed when considering the simulative Hamiltonian, with the EBH featuring its own hyper-parameter, under the canonical ensembles at different temperatures. Specifically, a discontinuity in bulk entropy at the BQP is observed. The exotic entropic distribution, the relations between the symmetries of Hamiltonian and BQP, and the impacts from the entanglement-bath dimension are also explored. Our results show that such a singularity differs from those in the conventional thermodynamic phase transition points that normally fall into the Landau–Ginzburg paradigm. Our work provides the opportunities on exploring the exotic phenomena induced by the competition between the bulk and boundaries.
Constructing quantum Hamiltonians for simulating and controlling the exotic physics of many-body systems belongs to the most important topics of condensed matter physics and quantum technologies. The main challenge that hinders the future investigations is the extremely high complexity for either their numerical simulations or experimental realizations. In this work, we propose the temperature-adaptive entanglement simulator (TAES) that mimics and tunes the thermodynamics of the one-dimensional (1D) many-body system by embedding a small-size model in an entanglement bath. The entanglement bath is described by the interactions located at the boundaries of the small-size model, whose coupling constants are optimized by means of differentiable tensor network at target temperatures. With the benchmark on 1D spin chains, TAES surpasses the state-of-the-art accuracy compared with the existing finite-temperature approaches such as linearized and differential tensor renormalization group algorithms. By tuning the couplings of the entanglement bath with the temperature fixed, the bulk entropy exhibits similar behavior compared to that obtained by tuning the temperature. Our work provides novel opportunities of engineering the distribution of fluctuations and mimicking the non-equilibrium phenomena in a uniform temperature within the canonical ensemble framework using the optimized boundary interactions.
In this work we propose to simulate many-body thermodynamics of infinite-size quantum lattice models in one, two, and three dimensions, in terms of few-body models of only O(10) sites, which we coin as quantum entanglement simulators (QES's). The QES is described by a temperature-independent Hamiltonian, with the boundary interactions optimized by the tensor network methods to mimic the entanglement between the bulk and environment in a finite-size canonical ensemble. The reduced density matrix of the physical bulk then gives that of the infinite-size canonical ensemble under interest. We show that the QES can, for instance, accurately simulate varieties of many-body phenomena, including finite-temperature crossover and algebraic excitations of the one-dimensional spin liquid, the phase transitions and low-temperature physics of the two- and three-dimensional antiferromagnets, and the crossovers of the two-dimensional topological system. Our work provides an efficient way to explore the thermodynamics of intractable quantum many-body systems with easily accessible systems.
We demonstrate the existence of topological phase transitions in interacting, symmetry-protected quantum matter at finite temperatures. Using a combined numerical and analytical approach, we study a one-dimensional Su-Schrieffer-Heeger model with added Hubbard interactions, where no thermodynamic phase transition occurs at finite temperatures. The transition is signalled by a quantized, nonlocal bulk topological order parameter. It is driven by defects, which are enabled by the combination of interaction and thermal activation, with no counterpart in the noninteracting limit. The defects localize topological zero modes, which, when sufficiently abundant, cause the order parameter to vanish. This phenomenon, interpreted via bulk-boundary correspondence, reflects the loss of a topological edge mode at a well-defined critical temperature in the thermodynamic limit. Unlike zero-temperature topological transitions, these finite-temperature transitions lack thermodynamic signatures but remain observable in controlled quantum systems, such as ultracold fermionic atoms in optical lattices.
Quantum phase transition arises in general as second order phase transition at zero temperature, tuned by a non-thermal parameter such as pressure, doping or a magnetic field. The point in the phase diagram of the material in which different phases meet is called a quantum critical point (QCP). Physics around QCPs are of extensive current interest because the critical quantum fluctuations influence the physical properties in a wide temperature range (quantum criticality), and are believed to be responsible for many emergent physical properties such as non-Fermi liquids and unconventional superconductivity. In this research we explore dynamics and thermodynamics near QCPs via investigating three classes of models, which all have real material correspondence. Specifically first, we study local dynamics in a perturbed quantum critical Ising chain with E8 symmetry, where we show the local dynamical spin susceptibility has a singular dependence on frequency, but differs from the diffusion form. The nuclear magnetic resonance (NMR) relaxation rate at low temperatures depends exponentially on the inverse temperature, whose prefactor we also determine. We propose NMR experiments as a means to further test the applicability of the E8 description for CoNb2O6. Second, we investigate the thermodynamic properties of itinerant ferromagnets near quantum critical points, described by the quantum Landau-Ginzburg theory. We provide a regularized perturbative renormalization group procedure to calculate the free energy. We further carry out numerical calculations on thermodynamic quantities, capturing not only the leading critical behaviors, but also the subleading and nonsingular contributions. We demonstrate various thermodynamic signatures of quantum criticality, including the entropy accumulation effect and the divergence of the specific heat coefficient. A detailed comparison to the recent experimental results on an itinerant ferromagnet Sr3Ru2O7 is also presented. Third, we explore Ising-nematic and magnetic phases and their transitions in iso-electronically doped iron pnictides by carrying out a large-N study of an effective low-energy Ginzburg-Landau model for these systems. We demonstrate that the magnetic and Ising orders transitions are concurrent at zero temperature, and both transitions are weakly first-order, which is consistent with RG-based prediction and experimental observations.
Quantum impurities can host exotic many-body states that serve as sensitive probes of bath correlations. However, quantitative and non-perturbative methods for determining impurity thermodynamics in such settings remain scarce. Here, we introduce an impurity renormalization group approach that merges the tensor-network representation with the numerical renormalization group cutoff scheme. This method overcomes conventional limitations by treating bath correlations and impurity interactions on an equal footing. Applying our approach to the finite-temperature quantum critical regime of quantum spin systems, we uncover striking impurity-induced phenomena. In a coupled Heisenberg ladder, the impurity triggers a fractionalization of the local magnetic moment. Moreover, the derivative of the impurity susceptibility develops cusps that mark the crossover into the quantum critical regime. We also observe an exotic evolution of the spin correlation function driven by the interplay between bath correlations and the impurity. Our results demonstrate that this method can efficiently solve correlated systems with defects, opening new pathways to discovering novel impurity physics beyond those in non-interacting thermal baths.
Exploring the role of entanglement in quantum nonequilibrium dynamics is important to understand the mechanism of thermalization in an isolated system. We study the relaxation dynamics in a one-dimensional extended Bose–Hubbard model after a global interaction quench by considering several observables: the local Boson numbers, the nonlocal entanglement entropy, and the momentum distribution functions. We calculate the thermalization fidelity for different quench parameters and different sizes of subsystems, and the results show that the degree of thermalization is affected by the distance from the integrable point and the size of the subsystem. We employ the Pearson coefficient as the measurement of the correlation between the entanglement entropy and thermalization fidelity, and a strong correlation is demonstrated for the quenched system.