Indicator Of Quantum Phase Transition Research Articles

Indicators of quantum phase transitions in the one-dimensional J1-J2 Heisenberg model: Global quantum discord and multipartite nonlocality analysis

We here investigate the ground state phase transitions of the one-dimensional J1-J2 Heisenberg model. The phase transition is characterized by analyzing the quantum discord, global quantum discord (GQD), bipartite nonlocality, and multipartite nonlocality of the ground state. Our findings reveal that these correlations serve as effective indicators of the phase transition point at J2/J1=0.5. Specifically, quantum discord and bipartite nonlocality display more pronounced critical behavior in small-sized systems. Conversely, for large-scale systems, GQD and multipartite nonlocality offer a more practical and reliable method for detecting many-body driven phase transitions. Additionally, several linear relationships among these correlations are identified.

Entropic uncertainty relations and quantum coherence in the two-dimensional XXZ spin model with Dzyaloshinskii–Moriya interaction

Quantum renormalization group (QRG) is a tractable method for studying the criticalities of one-dimensional (1D) and two-dimensional (2D) many-body systems. By employing the QRG method, we first derive the effective Hamiltonian and QRG equations of a 2D XXZ model with Dzyaloshinskii–Moriya (DM) interaction analytically. The linear-entropy-based uncertainty, the quantum discord (QD), and the multipartite quantum coherence based on the square root of the quantum Jensen–Shannon divergence of the 2D XXZ model are then studied as the indicators of quantum phase transitions (QPTs). The nonanalytic and scaling behaviors of the uncertainty, QD and quantum coherence are also analyzed through numerical calculations. Moreover, we investigate the effect of the easy-axis anisotropy parameter and DM interaction on the QPT. We find that the uncertainty, QD, and quantum coherence can all be utilized to detect QPTs. Our findings could shed new light on the observable of the QPT of the many-body system with the uncertainty and quantum coherence, and enrich the application of QRG method to Heisenberg spin models.

Average coherence and average correlated coherence as indicators of quantum phase transitions in the XY model with staggered Dzyaloshinskii-Moriya interaction

The performance of average coherence (AC) and average correlated coherence (ACC) in detecting quantum phase transitions (QPTs) has been explored by considering the XY model with staggered Dzyaloshinskii-Moriya interaction. By using the quantum renormalization group method, it is shown that the ground-state AC and ACC show either a maximum or a minimum at the QPT point. Moreover, the AC and ACC susceptibilities (i.e. their derivatives with respect to the driving parameter) have two extreme points near the two sides of the QPT point. A finite-scaling analysis reveals that these extreme points tend to the QPT point after several iterations of the renormalization and the susceptibilities at the QPT point become divergent in the thermodynamic limit.

Renormalization of net steered coherence and average coherence in the XXZ model with Dzyaloshinskii–Moriya interaction

The critical behaviors of the net steered coherence (NSC) and average coherence (AC) in the XXZ model with Dzyaloshinskii–Moriya interaction are investigated by adopting the quantum renormalization group method. It is found that they both develop different saturated values in different phases of the model after enough iterations of the renormalization of the coupling constants. In addition, their susceptibilities at the phase transition point are divergent in the thermodynamic limit, and the scaling exponent is determined by the exponent governing the divergence of the correlation length close to the phase transition point. This exemplifies that both the NSC and AC can serve as reliable indicators of quantum phase transitions.

Shared purity and concurrence of a mixture of ground and low-lying excited states as indicators of quantum phase transitions

We investigate the efficacy of shared purity, a measure of quantum correlation that is independent of the separability-entanglement paradigm, as a quantum phase transition indicator in comparison with concurrence, a bipartite entanglement measure. The order parameters are investigated for thermal states and pseudo-thermal states, of the systems considered. In the case of the one-dimensional J 1 − J 2 Heisenberg quantum spin model and the one-dimensional transverse-field quantum Ising model, shared purity turns out to be as effective as concurrence in indicating quantum phase transitions. In the two-dimensional J 1 − J 2 Heisenberg quantum spin model, shared purity indicates the two quantum phase transitions present in the model, while concurrence detects only one of them. Moreover, we find diverging finite-size scaling exponents for the order parameters near the transitions in odd- and even-sized systems governed by the one-dimensional J 1 − J 2 model, as had previously been reported for quantum spins on odd- and even-legged ladders. It is plausible that the divergence is related to a Möbius strip-like boundary condition required for odd-sized systems, while for even-sized systems, the usual periodic boundary condition is sufficient.

Uncertainty Relation and Quantum Phase Transition in the Two-Dimensional Ising Model

By using quantum renormalization group (QRG) approach, we first derive the effective Hamiltonian and QRG equations of the two-dimensional (2D) Ising models with two different time-dependent transverse magnetic fields analytically. Then we examine the nonanalytic and scaling behaviors of the linear-entropy-based uncertainty relation and quantum entanglement of the models near the critical point through numerical analysis. Moreover, we investigate the relation between the quantum critical point and the external magnetic field. Our results show that both the uncertainty relation and the quantum entanglement are feasible to detect the quantum phase transition (QPT), and the uncertainty relation may be a better indicator of QPT than quantum entanglement. Our findings could shed new light on the observable of the QPTs of the solid-state system with the uncertainty relation.

Operational definition of a quantum speed limit

The quantum speed limit is a fundamental concept in quantum mechanics, which aims at finding the minimum time scale or the maximum dynamical speed for some fixed targets. In a large number of studies in this field, the construction of valid bounds for the evolution time is always the core mission, yet the physics behind it and some fundamental questions like which states can really fulfill the target, are ignored. Understanding the physics behind the bounds is at least as important as constructing attainable bounds. Here we provide an operational approach for the definition of the quantum speed limit, which utilizes the set of states that can fulfill the target to define the speed limit. Its performances in various scenarios have been investigated. For time-independent Hamiltonians, it is inverse-proportional to the difference between the highest and lowest energies. The fact that its attainability does not require a zero ground-state energy suggests it can be used as an indicator of quantum phase transitions. For time-dependent Hamiltonians, it is shown that contrary to the results given by existing bounds, the true speed limit should be independent of the time. Moreover, in the case of spontaneous emission, we find a counterintuitive phenomenon that a lousy purity can benefit the reduction of the quantum speed limit.

Quantum Renormalization of Spin Squeezing in Spin Chains

By employing quantum renormalization group (QRG) method, we investigate quantum phase transitions (QPT) in the Ising transverse field (ITF) model and in the XXZ Heisenberg model, with and without Dzyaloshinskii Moriya (DM) interaction, on a periodic chain of N lattice sites. We adopt a new approach called spin squeezing as an indicator of QPT. Spin squeezing, through analytical expression of a spin squeezing parameter, is calculated after each step of QRG. As the scale of the system becomes larger, (after many QRG steps), the ground state (GS) spin squeezing parameters show an abrupt change at a quantum critical point (QCP). Moreover, in all of the studied models, the first derivative of the spin squeezing parameter with respect to the control parameter is discontinuous, which is a signature of QPT. The spin squeezing parameters develop their saturated values after enough QRG iterations. The divergence exponent of the first derivative of the spin squeezing parameter in the near vicinity of the QCP is associated with the critical exponent of the correlation length.

Quantum coherence as indicators of quantum phase transitions, factorization and thermal phase transitions in the anisotropic XY model

Quantifying quantum coherence has attracted considerable interests. In the present work, we employ two measures of quantum coherence recently proposed in terms of the skew information and the trace norm, respectively, to investigate the quantum phase transitions (QPTs), factorization in the XY model and the thermal phase transitions (TPTs) in the transverse field Ising model. Two quantifications of quantum nonlocality via the same distance measure of the quantum coherence are also studied for reference. It is shown that two types of quantum coherence are reliable in identifying QPTs and TPTs. However, only the quantum coherence based on the skew information can detect factorization. In addition, the quantum coherence and nonlocality measured via the same distance space have similar finite temperature scaling law, while the quantum coherence based on skew information and trace norm has different finite temperature scaling law. Moreover, the skew-information-based quantum coherence at finite temperature suggests that factorization vanishes when temperature exceeds 0.02 (Boltzmann constant $$k_{B} = 1$$ ), which is in agreement with the results of the fidelity for states with different distances of spin-pairs.

Thermal quantum coherence and correlation in the extended XY spin chain

Quantum coherence and correlation of thermal states in the extended XY spin chain are studied in terms of the recently proposed l1 norm, skew information, and Bures distance of geometry discord (BGD), respectively. The entanglement measured via concurrence is calculated for reference. A two-dimensional susceptibility is introduced to explore their capability in highlighting the critical lines associated with quantum phase transitions in the model. It is shown that the susceptibility of the skew information and BGD is a genuine indicator of quantum phase transitions, and characterizes the factorization. However, the l1 norm is trivial for the factorization. An explicit scaling law of BGD is captured at low temperature in the XY model. In contrast to the entanglement, quantum coherence reveals a kind of long-range nonclassical correlation. Moreover, the obvious relation among model parameters is extracted for the factorized line in the extended model. Those are instructive for the understanding of quantum coherence and correlation in the theory of quantum information, and quantum phase transitions and factorization in condensed-matter physics.

Genuine multipartite entanglement as the indicator of quantum phase transition in spin systems

In this paper, the genuine multipartite entanglement (GME) and quantum criticality property of spin systems with staggered Dzyaloshinskii---Moriya (DM) interaction are investigated by exploiting quantum renormalization group method. The results show that the GME can indicate quantum phase transitions at critical points after several iterations of the renormalization. Moreover, the DM interaction effectively restores the spoiled GME via creation of quantum fluctuations, while it also changes the critical points. At last, the nonanalytic and scaling behaviors of GME are analyzed in detail.

Entanglement and quantum phase transition of spin glass: A renormalization group approach

Abstract Using a renormalization group approach, we study the entanglement properties of two spin glass models: the XXZ Heisenberg (with Dzyaloshinskii–Moriya interaction) and Ising transverse field spin glasses. The concurrence for both models are obtained through the Kadanoff renormalization group (RG) approach with random J i z and J i respectively. The constant couplings in the RG flow are randomized through the Gaussian distribution. For Δ = 0 corresponding to a non-spin glass material, a first-order transition is expected. By varying Δ from 0.05 to 0.5, the spin glass effect broadens the sharp transition resulting in a second-order-like transition. The fluctuations in the average concurrence for the spin glass case as measured by the standard deviations is also a good indicator of quantum phase transition.

Nonuniversality of entanglement convertibility

Recently, it has been suggested that operational properties connected to quantum computation can be alternative indicators of quantum phase transitions. In this work we systematically study these operational properties in 1D systems that present phase transitions of different orders. For this purpose, we evaluate the local convertibility between bipartite ground states. Our results suggest that the operational properties, related to non-analyticities of the entanglement spectrum, are good detectors of explicit symmetries of the model, but not necessarily of phase transitions. We also show that thermodynamically equivalent phases, such as Luttinger liquids, may display different convertibility properties depending on the underlying microscopic model.

Quantum Dissonance as an Indicator of Quantum Phase Transition in the XXZ Chain

We investigate the behavior of quantum dissonance in the anti-ferromagnetic XXZ spin S = 1/2 chain, which exhibits a quantum phase transition. Based on a unified view of quantum and classical correlations, quantum dissonance is analytically calculated and is compared with entanglement, discord, and classical correlations for the ground state of the system. It is found that the nearest-neighbor quantum dissonance achieves an extremum and exhibits the sharpest change at the critical point. Therefore, quantum dissonance may serve as a more efficient indicator of quantum phase transitions in the XXZ spin chain.

Quantum fidelity for degenerate ground states in quantum phase transitions

Spontaneous symmetry breaking in quantum phase transitions leads to a system having degenerate ground states in its broken-symmetry phase. In order to detect all possible degenerate ground states for a broken-symmetry phase, we introduce a quantum fidelity defined as an overlap measurement between a system ground state and an arbitrary reference state. If a system has N-fold degenerate ground states in a broken-symmetry phase, the quantum fidelity is shown to have N different values with respect to an arbitrarily chosen reference state. The quantum fidelity then exhibits an N-multiple bifurcation as an indicator of a quantum phase transition without knowing any detailed broken symmetry between a broken-symmetry phase and a symmetry phase as a system parameter crosses its critical value (i.e., a multiple bifurcation point). Each order parameter, characterizing a broken-symmetry phase from each degenerate ground state reveals an N-multiple bifurcation. Furthermore, it is shown that it is possible to specify how each order parameter calculated from degenerate ground states transforms under a subgroup of a symmetry group of the Hamiltonian. Examples are given through study of the quantum q-state Potts models with a transverse magnetic field by employing tensor network algorithms based on infinite-size lattices. For any q, a general relation between the local order parameters is found to clearly show the subgroup of the Z_{q} symmetry group. In addition, we systematically discuss criticality in the q-state Potts model.

Correlation and nonlocality measures as indicators of quantum phase transitions in several critical systems

We have investigated the quantum phase transitions in the ground states of several critical systems, including transverse field Ising and XY models as well as XY with multiple spin interactions, XXZ and the collective system Lipkin–Meshkov–Glick models, by using different quantumness measures, such as entanglement of formation, quantum discord, as well as its classical counterpart, measurement-induced disturbance and the Clauser–Horne–Shimony–Holt–Bell function. Measurement-induced disturbance is found to detect the first and second order phase transitions present in these critical systems, while, surprisingly, it is found to fail to signal the infinite-order phase transition present in the XXZ model. Remarkably, the Clauser–Horne–Shimony–Holt–Bell function is found to detect all the phase transitions, even when quantum and classical correlations are zero for the relevant ground state.

Quantum phases with differing computational power

The observation that concepts from quantum information has generated many alternative indicators of quantum phase transitions hints that quantum phase transitions possess operational significance with respect to the processing of quantum information. Yet, studies on whether such transitions lead to quantum phases that differ in their capacity to process information remain limited. Here we show that there exist quantum phase transitions that cause a distinct qualitative change in our ability to simulate certain quantum systems under perturbation of an external field by local operations and classical communication. In particular, we show that in certain quantum phases of the XY model, adiabatic perturbations of the external magnetic field can be simulated by local spin operations, whereas the resulting effect within other phases results in coherent non-local interactions. We discuss the potential implications to adiabatic quantum computation, where a computational advantage exists only when adiabatic perturbation results in coherent multi-body interactions.

Entanglement Entropy Signature of Quantum Phase Transitions in a Multiple Spin Interactions Model

Through the Jordan—Wigner transformation, the entanglement entropy and ground state phase diagrams of exactly solvable spin model with alternating and multiple spin exchange interactions are investigated by means of Green's function theory. In the absence of four-spin interactions, the ground state presents plentiful quantum phases due to the multiple spin interactions and magnetic fields. It is shown that the two-site entanglement entropy is a good indicator of quantum phase transition (QPT). In addition, the alternating interactions can destroy the magnetization plateau and wash out the spin-gap of low-lying excitations. However, in the presence of four-spin interactions, apart from the second order QPTs, the system manifests the first order QPT at the tricritical point and an additional new phase called “spin waves”, which is due to the collapse of the continuous tower-like low-lying excitations modulated by the four-spin interactions for large three-spin couplings.

Field-controlled magnetic order with insulator–metal transitions in a periodic Anderson-like organic polymer

The zero- and low-temperature behaviors of a quasi-one-dimensional organic polymer proposed as a symmetrical periodic Anderson-like chain model, in which the localized f orbitals hybridize with the conduction orbitals at even sites, are investigated by means of many-body Green's function theory. In the absence of magnetic field, the ground state of the system turns out to be ferrimagnetic. The temperature-induced phase diagrams have been explored, where the competition between the Hubbard repulsion U on the localized f orbital and the hybridization strength V makes an important impact on the transition temperature. In a magnetic field, it is found that a 1/3 magnetization plateau appears and two critical fields indicating the insulator-metal transitions at zero temperature emerge, which are closely related to the energy bands. Furthermore, the single-site entanglement entropy is a good indicator of quantum phase transitions. The temperature-field-induced phase diagram has also been attained, wherein the magnetization plateau state, the gapless phase and the spin polarized state are revealed. The temperature dependence of thermodynamic quantities such as the magnetization, susceptibility and specific heat are calculated to characterize the corresponding phases. It is also found that the up-spin and down-spin hole excitations are responsible for the thermodynamic properties.

Multipartite entanglement and quantum phase transitions in the one-, two-, and three-dimensional transverse-field Ising model

In this paper we consider the quantum phase transition in the Ising model in the presence of a transverse field in one, two and three dimensions from a multi-partite entanglement point of view. Using \emph{exact} numerical solutions, we are able to study such systems up to 25 qubits. The Meyer-Wallach measure of global entanglement is used to study the critical behavior of this model. The transition we consider is between a symmetric GHZ-like state to a paramagnetic product-state. We find that global entanglement serves as a good indicator of quantum phase transition with interesting scaling behavior. We use finite-size scaling to extract the critical point as well as some critical exponents for the one and two dimensional models. Our results indicate that such multi-partite measure of global entanglement shows universal features regardless of dimension $d$. Our results also provides evidence that multi-partite entanglement is better suited for the study of quantum phase transitions than the much studied bi-partite measures.