Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1906.06553 · Physical review. B./Physical review. B

Intrinsic jump character of first-order quantum phase transitions

Qiang Luo, Jize Zhao, Xiaoqun Wang

Published Sep 26, 2019• 22 citations
arXivHTMLPDF

Abstract

We find that the first-order quantum phase transitions (QPTs) are characterized by intrinsic jumps of relevant operators while the continuous ones are not. Based on such an observation, we propose a bond reversal method where a quantity $\mathcal{D}$, the difference of bond strength (DBS), is introduced to judge whether or not a QPT is of first order. This method is first applied to an exactly solvable spin-$1/2$ XXZ Heisenberg chain and a quantum Ising chain with a longitudinal field where distinct jumps of $\mathcal{D}$ appear at the first-order transition points for both cases. We then use it to study the topological QPT of a cross-coupled (${J}_{\ifmmode\times\else\texttimes\fi{}}$) spin ladder where the Haldane--rung-singlet transition switches from being continuous to exhibiting a first-order character at ${J}_{\ifmmode\times\else\texttimes\fi{},I}\ensuremath{\simeq}0.30(2)$. Finally, we study a recently proposed one-dimensional analogy of a deconfined quantum critical point connecting two ordered phases in a spin-$1/2$ chain. We rule out the possibility of a weakly first-order QPT because the DBS is smooth when crossing the transition point. Moreover, we affirm that such a transition belongs to the Gaussian universality class with a central charge $c=1$.

DOI
10.1103/physrevb.100.121111

Related papers

Topological quantum phase transition in bond-alternating spin- 12 Heisenberg chains

Hai Tao Wang, Bo Li, Sam Young Cho

We investigate string correlations in an infinite-size spin-1/2 bond-alternating Heisenberg chain. By employing the infinite matrix product state representation with the infinite time evolving block decimation method, a finite string correlation for extremely large lattice distances is directly observed, in contrast to an extrapolated extreme value for finite size chains. We find that a topological quantum phase transition occurs between two different phases separated and characterized by two different long-range string orders in the space of bond-alternating interactions. Also, the critical exponent $\ensuremath{\beta}$ from the long-range string orders is obtained as $\ensuremath{\beta}=1/12$ and the central charge at the critical point is obtained as $c\ensuremath{\simeq}1$, which shows that the topological phase transition belongs to the Gaussian universality class. In addition, it is shown that, for the topological quantum phase transition, the phase boundary can be captured by the singular behavior of the von Neumann entropy and the pinch point of the fidelity per site.

arXiv:1210.5453•Physical Review B•Feb 4, 2013•48 citations

Quantum entanglement and critical exponents in one-dimensional spin-1 bond-alternating XXZ chains

Yaoheng Su, Chen Ai-Min, Honglei Wang +1 more

The characterization of the quantum phase transition in a lowdimensional system has attracted a considerable amount of attention in quantum manybody systems. As one of the fundamental models in quantum magnetism, spin-1 models have richer phase diagrams and show more complex physical phenomena. In the spin-1 antiferromagnetic XXZ model, the Haldane phase and the Nel phase are the gapped topologic phases which cannot be characterized by the local order parameters. To characterize the nature in such phases, one has to calculate the non-local long range order parameters. Normally, the non-local order parameter in the topological phase is obtained from the extrapolation of finite-sized system in numerical study. However, it is difficult to extract the critical exponents with such an extrapolated non-local order parameter due to the numerical accuracy. In a recently developed tensor network representation, i.e., the infinite matrix product state (iMPS) algorithm, it was shown that the non-local order can be directly calculated from a very large lattice distance in an infinite-sized system rather than an extrapolated order parameter in a finite-sized system. Therefore, it is worthwhile using this convenient technique to study the non-local orders in the topological phases and characterize the quantum criticalities in the topological quantum phase transitions. In this paper, by utilizing the infinite matrix product state algorithm based on the tensor network representation and infinite time evolving block decimation method, the quantum entanglement, fidelity, and critical exponents of the topological phase transition are investigated in the one-dimensional infinite spin-1 bond-alternating XXZ Heisenberg model. It is found that there is always a local dimerization order existing in the whole parameter range when the bond-alternative strength parameter changes from 0 to 1. Also, due to the effect of the bond-alternating, there appears a quantum phase transition from the long-rang ordering topological Nel phase to the local ordering dimerization phase. The von Neumann entropy, fidelity per lattice site, and order parameters all give the same phase transition point at c = 0.638. To identify the type of quantum phase transition, the central charge c 0.5 is extracted from the ground state von Neumann entropy and the finite correlation length, which indicates that the phase transition belongs to the two-dimensional Ising universality class. Furthermore, it is found that the Nel order and the susceptibility of Nel order have power-law relations to |-c|. From the numerical fitting of the Nel order and its susceptibility, we obtain the characteristic critical exponents ' = 0.236 and ' = 0.838. It indicates that such critical exponents from our method characterize the nature of the quantum phase transition. Our critical exponents from the iMPS method can provide guidance for studying the properties of the phase transition in quantum spin systems.

Acta Physica Sinica•Jan 1, 2017•2 citations

Bond-Alternation-Induced Topological Quantum Gaussian Transition and Topological Quantum Crossover in Ising Chains with the Dzyaloshinskii-Moriya Interaction

Hai Tao Wang, Sam Young Cho

Non-local orders, entanglement entropy, and quantum fidelity are investigated in an infinite-size bond-alternating Ising chain with the Dzyaloshinskii-Moriya interaction by employing the infinite matrix product state representation with the infinite time evolving block decimation method. Directly computing two distinct types of finite string correlations for very large lattice distances, in contrast to an extrapolated extreme value for finite size chains, reveals two topologically ordered phases. As the bond alternation varies, a topological quantum phase transition with continuously variable critical exponents along the phase boundary occurs between the two Haldane phases for a Dzyaloshinskii-Moriya interaction stronger than the Ising interaction while a topological quantum crossover between them happens through an intermediate antiferromagentic phase demonstrated with the quantum fidelity for a Dzyaloshinskii-Moriya interaction weaker than the Ising interaction. The critical exponents of the order parameters and the central charges from the entanglement entropy quantify the universality classes of the phase transition points. Anisotropic Heisenberg types of spin chains with bond alternations are finally discussed to share the same criticality.

arXiv:1310.3169•Journal of the Korean Physical Society•Nov 19, 2020•0 citations

Mixed-order transition in the antiferromagnetic quantum Ising chain in a field

Péter Lajkó, Ferenc Iglói

The antiferromagnetic quantum Ising chain has a quantum critical point which belongs to the universality class of the transverse Ising model (TIM). When a longitudinal field ($h$) is switched on, the phase transition is preserved, which turns to first order for $h/\mathrm{\ensuremath{\Gamma}}\ensuremath{\rightarrow}\ensuremath{\infty}, \mathrm{\ensuremath{\Gamma}}$ being the strength of the transverse field. Here we will re-examine the critical properties along the phase transition line. During a quantum block renormalization group calculation, the TIM fixed point for $h/\mathrm{\ensuremath{\Gamma}}>0$ is found to be unstable. Using DMRG techniques, we calculated the entanglement entropy and the spin-spin correlation function, both of which signaled a divergent correlation length at the transition point with the TIM exponents. At the same time, the bulk correlation function has a jump and the end-to-end correlation function has a discontinuous derivative at the transition point. Consequently for finite $h/\mathrm{\ensuremath{\Gamma}}$ the transition is of mixed order.

arXiv:2012.07470•Physical review. B./Physical review. B•May 4, 2021•9 citations

Quantum phase transitions and hidden topological order in one-dimensionalS=1 Heisenberg–Ising alternating model

Guanghua Liu, Longjuan Kong, Xiaoyan Deng +1 more

By the infinite time-evolving block decimation method, the ground state properties of the S=1 Heisenberg–Ising alternating chain have been investigated in the thermodynamic limit. A ground-state phase diagram, which includes three different phases, i.e., an antiferromagnetic strip phase, a dimer phase, and an antiferromagnetic phase, is obtained. A modified definition of the string order is adopted to describe the dimer phase, and it is found to have nonzero antiferromagnetic topological string order. The quantum phase transitions (QPTs) in such a model can be well described by the singularities of bipartite entanglement and fidelity bifurcations, and two second-order QPTs points are determined to be at JI≃±0.66983. The central charges at both QPTs points are determined to be ∼1/2. Therefore, both QPTs belong to the Ising universality class with central charges c=c‾=1/2.

Phase Transitions•Mar 16, 2015•1 citation

First-order excited-state quantum phase transition in the transverse Ising model with a longitudinal field

Yun-Tong Yang, Hong‐Gang Luo

Abstract Investigations into first-order quantum phase transition (QPT) remain unclear in comparison to those of the second-order or continuous QPT, in which the order parameter and associated broken symmetry can be clearly identified and, at the same time, the concepts of universality class and critical scaling can be characterized by critical exponents. Here, we present a comparison study of these two kinds of QPT in the transverse Ising model; the emphasis is on the first-order QPT. In the absence of a longitudinal field, the ground state of the model exhibits a second-order QPT from the paramagnetic phase to the ferromagnetic phase, which is smeared out once the longitudinal field is applied. Surprisingly, the first excited state involves a first-order QPT as the longitudinal field increases, which has not been reported in the literature. Within the framework of the pattern picture, we clearly identify the difference between these two kinds of QPT: for the continuous QPT, only the pattern flavoring the ferromagnetic phase is always dominant over the others. By contrast, there are at least two competitive patterns in the first-order QPT, which is further indicated by the patterns’ occupancies, calculated by pattern projections on the ground- and first excited-state wavefunctions. Our results not only have a fundamental significance in the understanding of the nature of QPTs, but also a practical interest in quantum simulations used to test the present findings.

arXiv:2301.02066•Communications in Theoretical Physics•Aug 6, 2025•1 citation
We find that the first-order quantum phase transitions (QPTs) are characterized by intrinsic jumps of relevant operators while the continuous ones are not. Based on such an observation, we propose a bond reversal method where a quantity D\mathcal{D}D, the difference of bond strength (DBS), is introduced to judge whether or not a QPT is of first order. This method is first applied to an exactly solvable spin-1/21/21/2 XXZ Heisenberg chain and a quantum Ising chain with a longitudinal field where distinct jumps of D\mathcal{D}D appear at the first-order transition points for both cases. We then use it to study the topological QPT of a cross-coupled (J\ifmmode×\else\texttimes\fi{J}_{\ifmmode\times\else\texttimes\fi{}}J\ifmmode×\else\texttimes\fi​) spin ladder where the Haldane--rung-singlet transition switches from being continuous to exhibiting a first-order character at J\ifmmode×\else\texttimes\fi,I\ensuremath≃0.30(2){J}_{\ifmmode\times\else\texttimes\fi{},I}\ensuremath{\simeq}0.30(2)J\ifmmode×\else\texttimes\fi,I​\ensuremath≃0.30(2). Finally, we study a recently proposed one-dimensional analogy of a deconfined quantum critical point connecting two ordered phases in a spin-1/21/21/2 chain. We rule out the possibility of a weakly first-order QPT because the DBS is smooth when crossing the transition point. Moreover, we affirm that such a transition belongs to the Gaussian universality class with a central charge c=1c=1c=1.
We investigate string correlations in an infinite-size spin-1/2 bond-alternating Heisenberg chain. By employing the infinite matrix product state representation with the infinite time evolving block decimation method, a finite string correlation for extremely large lattice distances is directly observed, in contrast to an extrapolated extreme value for finite size chains. We find that a topological quantum phase transition occurs between two different phases separated and characterized by two different long-range string orders in the space of bond-alternating interactions. Also, the critical exponent $\ensuremath{\beta}$ from the long-range string orders is obtained as $\ensuremath{\beta}=1/12$ and the central charge at the critical point is obtained as $c\ensuremath{\simeq}1$, which shows that the topological phase transition belongs to the Gaussian universality class. In addition, it is shown that, for the topological quantum phase transition, the phase boundary can be captured by the singular behavior of the von Neumann entropy and the pinch point of the fidelity per site.
The characterization of the quantum phase transition in a lowdimensional system has attracted a considerable amount of attention in quantum manybody systems. As one of the fundamental models in quantum magnetism, spin-1 models have richer phase diagrams and show more complex physical phenomena. In the spin-1 antiferromagnetic XXZ model, the Haldane phase and the Nel phase are the gapped topologic phases which cannot be characterized by the local order parameters. To characterize the nature in such phases, one has to calculate the non-local long range order parameters. Normally, the non-local order parameter in the topological phase is obtained from the extrapolation of finite-sized system in numerical study. However, it is difficult to extract the critical exponents with such an extrapolated non-local order parameter due to the numerical accuracy. In a recently developed tensor network representation, i.e., the infinite matrix product state (iMPS) algorithm, it was shown that the non-local order can be directly calculated from a very large lattice distance in an infinite-sized system rather than an extrapolated order parameter in a finite-sized system. Therefore, it is worthwhile using this convenient technique to study the non-local orders in the topological phases and characterize the quantum criticalities in the topological quantum phase transitions. In this paper, by utilizing the infinite matrix product state algorithm based on the tensor network representation and infinite time evolving block decimation method, the quantum entanglement, fidelity, and critical exponents of the topological phase transition are investigated in the one-dimensional infinite spin-1 bond-alternating XXZ Heisenberg model. It is found that there is always a local dimerization order existing in the whole parameter range when the bond-alternative strength parameter changes from 0 to 1. Also, due to the effect of the bond-alternating, there appears a quantum phase transition from the long-rang ordering topological Nel phase to the local ordering dimerization phase. The von Neumann entropy, fidelity per lattice site, and order parameters all give the same phase transition point at c = 0.638. To identify the type of quantum phase transition, the central charge c 0.5 is extracted from the ground state von Neumann entropy and the finite correlation length, which indicates that the phase transition belongs to the two-dimensional Ising universality class. Furthermore, it is found that the Nel order and the susceptibility of Nel order have power-law relations to |-c|. From the numerical fitting of the Nel order and its susceptibility, we obtain the characteristic critical exponents ' = 0.236 and ' = 0.838. It indicates that such critical exponents from our method characterize the nature of the quantum phase transition. Our critical exponents from the iMPS method can provide guidance for studying the properties of the phase transition in quantum spin systems.
Non-local orders, entanglement entropy, and quantum fidelity are investigated in an infinite-size bond-alternating Ising chain with the Dzyaloshinskii-Moriya interaction by employing the infinite matrix product state representation with the infinite time evolving block decimation method. Directly computing two distinct types of finite string correlations for very large lattice distances, in contrast to an extrapolated extreme value for finite size chains, reveals two topologically ordered phases. As the bond alternation varies, a topological quantum phase transition with continuously variable critical exponents along the phase boundary occurs between the two Haldane phases for a Dzyaloshinskii-Moriya interaction stronger than the Ising interaction while a topological quantum crossover between them happens through an intermediate antiferromagentic phase demonstrated with the quantum fidelity for a Dzyaloshinskii-Moriya interaction weaker than the Ising interaction. The critical exponents of the order parameters and the central charges from the entanglement entropy quantify the universality classes of the phase transition points. Anisotropic Heisenberg types of spin chains with bond alternations are finally discussed to share the same criticality.
The antiferromagnetic quantum Ising chain has a quantum critical point which belongs to the universality class of the transverse Ising model (TIM). When a longitudinal field (hhh) is switched on, the phase transition is preserved, which turns to first order for $h/\mathrm{\ensuremath{\Gamma}}\ensuremath{\rightarrow}\ensuremath{\infty}, \mathrm{\ensuremath{\Gamma}}$ being the strength of the transverse field. Here we will re-examine the critical properties along the phase transition line. During a quantum block renormalization group calculation, the TIM fixed point for $h/\mathrm{\ensuremath{\Gamma}}>0$ is found to be unstable. Using DMRG techniques, we calculated the entanglement entropy and the spin-spin correlation function, both of which signaled a divergent correlation length at the transition point with the TIM exponents. At the same time, the bulk correlation function has a jump and the end-to-end correlation function has a discontinuous derivative at the transition point. Consequently for finite $h/\mathrm{\ensuremath{\Gamma}}$ the transition is of mixed order.
By the infinite time-evolving block decimation method, the ground state properties of the S=1 Heisenberg–Ising alternating chain have been investigated in the thermodynamic limit. A ground-state phase diagram, which includes three different phases, i.e., an antiferromagnetic strip phase, a dimer phase, and an antiferromagnetic phase, is obtained. A modified definition of the string order is adopted to describe the dimer phase, and it is found to have nonzero antiferromagnetic topological string order. The quantum phase transitions (QPTs) in such a model can be well described by the singularities of bipartite entanglement and fidelity bifurcations, and two second-order QPTs points are determined to be at JI≃±0.66983. The central charges at both QPTs points are determined to be ∼1/2. Therefore, both QPTs belong to the Ising universality class with central charges c=c‾=1/2.
Abstract Investigations into first-order quantum phase transition (QPT) remain unclear in comparison to those of the second-order or continuous QPT, in which the order parameter and associated broken symmetry can be clearly identified and, at the same time, the concepts of universality class and critical scaling can be characterized by critical exponents. Here, we present a comparison study of these two kinds of QPT in the transverse Ising model; the emphasis is on the first-order QPT. In the absence of a longitudinal field, the ground state of the model exhibits a second-order QPT from the paramagnetic phase to the ferromagnetic phase, which is smeared out once the longitudinal field is applied. Surprisingly, the first excited state involves a first-order QPT as the longitudinal field increases, which has not been reported in the literature. Within the framework of the pattern picture, we clearly identify the difference between these two kinds of QPT: for the continuous QPT, only the pattern flavoring the ferromagnetic phase is always dominant over the others. By contrast, there are at least two competitive patterns in the first-order QPT, which is further indicated by the patterns’ occupancies, calculated by pattern projections on the ground- and first excited-state wavefunctions. Our results not only have a fundamental significance in the understanding of the nature of QPTs, but also a practical interest in quantum simulations used to test the present findings.