Vector chiral order and dynamical quantum phase transitions in an Ising chain with dimerized anisotropic Gamma interaction

arXiv:2610.01167 · quant-ph, cond-mat.mes-hall · Submitted 2026-10-01 · Read on arXiv

Listen

Radio episode about this paper

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Vector chiral order and dynamical quantum phase transitions in an Ising chain with dimerized anisotropic Gamma interaction".

Mira: The gist: The competition between Gamma anisotropy and transverse field in an Ising chain leads to vector chiral order and dynamical quantum phase transitions,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So we're looking at this paper now titled "Vector chiral order and dynamical quantum phase transitions in an Ising chain with dimerized anisotropic Gamma interaction." Basically, it investigates a transverse-field Ising chain that has these specific staggered interactions, and they find that the competition between the Gamma anisotropy and the transverse field leads to some vector chiral order and these dynamical quantum phase transitions.

Mira: Right, so it’s not just looking at static ordering anymore; they’re seeing how dynamics come into play when you have this kind of interaction structure, which is interesting because it suggests that equilibrium ordering isn't the whole story. This study claims that this competition gives rise to positive and negative vector chiral phases alongside a paramagnetic phase defined by the vector spin chirality and the vector chiral order parameter.

Lev: From an error correction standpoint, if you were trying to run this on real hardware, you'd be looking at how stable those chiral orders are under noise. The paper points out that in the absence of Ising interactions, there’s a gapless critical line where things behave differently than standard Ising criticality because it shows no finite-size drift in spin correlations and subsystem entanglement entropy.

Kai: That sounds like a really important finding for understanding how these systems transition, even when they aren't exhibiting the standard behavior we expect from simpler models. They also found that the critical times for these dynamical quantum phase transitions follow periodic or aperiodic sequences depending on the quench path you take through the system.

Mira: And that periodicity in critical times is something to think about because it ties directly into how quickly you’re driving the system across those transition points, which is key for any real-time simulation. They also characterized this quantum phase using a staggered chiral order parameter called Oxystag, which relates directly to the antisymmetric connected spin correlation function Cxyr by saying Oxystag equals negative one times Cxyr at odd sites.

Lev: If we take that relationship seriously, it means you can track this order parameter using observable correlation functions like that Cxyr to see when those transitions happen in a simulation setup. The paper also found that the vector spin chirality decays algebraically at all three critical points, with η being approximately one/four for the case where alpha equals zero point five.

Kai: And on top of that, they measured the subsystem entanglement entropy and it grows logarithmically with the size L in the bulk interval, following a form like SL equals c times lnL plus s0. The extracted central charges are around one-half for both critical points when alpha is zero point five, which lines up with standard Ising criticality.

Mira: But there’s another detail they mention: at the critical line where alpha equals negative one and there are no Ising interactions, the excitation spectrum shows two gapless nodes with linear dispersion near them. That adds another layer of complexity to the physics described in this paper on vector chiral order and dynamical quantum phase transitions in an Ising chain with dimerized anisotropic Gamma interaction.

Paper summary: Lev: From a hardware perspective, those gapless nodes mean there’s still some low-energy behavior even at the critical point, which is something you have to be careful about when trying to implement this kind of physics in physical systems. They also noted that the authors themselves flagged that while they explored these things thoroughly, they didn't fully settle on the nature of every single gapless line.

Kai: So what does this mean for us who just listen? It means that adding these dimerized off-diagonal exchanges to a basic Ising model doesn't just change the static picture; it fundamentally alters how the system evolves over time and what kinds of ordering you can expect in equilibrium, especially when you introduce this transverse field.

Mira: Exactly. The paper shows that this specific type of interaction structure is a mechanism for enriching both the equilibrium phase structure and the dynamical critical behavior of quantum Ising chains, which gives us new ways to think about how these systems behave under different conditions.

Lev: It suggests that when you're looking at dynamical quantum phase transitions, you can expect these periodic or aperiodic sequences in critical times depending on your quench path, which is useful for designing experiments that probe these dynamics.

Kai: So we’ve covered the summary of this paper on Vector chiral order and dynamical quantum phase transitions in an Ising chain with dimerized anisotropic Gamma interaction. Now we're going to talk about what it actually means for the broader picture.

Mira: Let's shift gears a bit and look at the authors, Yu-Hong Yan, Shi-Qiao Wu, and Kun-Liang Zhang. They’ve done a lot of work in this area connecting different aspects of quantum criticality in chain systems.

Lev: If you were to take these findings and try to run them on actual quantum hardware, you'd be focusing on the stability of those chiral orders under noise and making sure your measurement setup can resolve those specific correlation functions they discussed.

Kai: That makes sense because the paper is so focused on these vector chiral order parameters; you need good tools to measure that stuff reliably. It’s about seeing if this complex ordering actually manifests in a physical system we can build.

Mira: The implication here is that dimerized off-diagonal exchange isn't just a mathematical trick; it's a real physical mechanism for generating richer phase structures and more complex dynamics in quantum magnets.

Lev: It gives us concrete ideas about how to engineer the interactions in a chain to get these specific dynamical transition behaviors, like those sequences of critical times they found.

Kai: So that’s what we’ve covered on Vector chiral order and dynamical quantum phase transitions in an Ising chain with dimerized anisotropic Gamma interaction. We hope this gives you a clearer picture of the physics being explored in this paper.

Conclusion: Kai: So, we’re wrapping up this look at "Vector chiral order and dynamical quantum phase transitions in an Ising chain with dimerized anisotropic Gamma interaction." Basically, these authors are showing how adding specific staggered interactions to a standard Ising model creates new types of magnetic ordering and new ways the system moves through its phases over time.

Mira: Right, they’re really focusing on how that competition between the anisotropy and the transverse field sets up these vector chiral phases, which are different from what you see in simple models. It suggests that equilibrium isn't just about one kind of ordering anymore; there are positive and negative versions of this chiral state.

Lev: For me, what’s interesting is how they link those static phase structures to the dynamics—they use something called Loschmidt amplitudes to predict when these quantum phase transitions will actually happen in real time. It moves it from just finding pictures of phases to predicting how the system *behaves* while it’s changing.

Kai: So, if we boil it down, this paper is about how these specific interactions unlock richer behavior in quantum chains than we saw before and shows us the connection between static ordering and dynamic transitions. It really brings together different ways we study these magnets.

Mira: And the main point for me is that this mechanism of dimerized off-diagonal exchange isn't just a small detail; it’s a core way to enrich both the equilibrium phase diagram and how you analyze the system when you are quenching it.

Lev: From an engineering side, those dynamical transitions mean we have to be careful about how fast we drive our physical systems across these critical points because the critical times they predict can be really sensitive to your starting point.

Kai: So, that's the big picture—we have new static ordering possibilities and a clearer map for predicting dynamic behavior in Ising chains with these complex interactions. We’re going to look at how those actual measurements would work next.

Yu-Hong Yan, Shi-Qiao Wu, Kun-Liang Zhang

School of Physics and Optoelectronic Engineering, Foshan University

quant-ph, cond-mat.mes-hall

Submitted: 2026-10-01

Updated: 2026-10-01

Comments: 10 pages, 6 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 77/100

The gist: The gist: The competition between Gamma anisotropy and transverse field in an Ising chain leads to vector chiral order and dynamical quantum phase transitions, enriching both equilibrium ordering and

Key concepts

Vector Chiral Order
This refers to a specific type of ordering in the system where the spin structure has a net chirality, meaning it has a preferred direction or sense (positive or negative) across different parts of the chain. It is quantified by an order parameter called Oxystag, which relates to antisymmetric spin correlations.
Dynamical Quantum Phase Transitions (DQPTs)
These transitions describe how the system's behavior changes over time when subjected to a quench. The paper analyzes this using the Loschmidt amplitude, which measures how close the evolved state is to the initial state. Critical points are found where this amplitude exhibits specific zeros.
Loschmidt Amplitude G(t)
This function tracks the evolution of a quantum system after it has been suddenly changed (quenched). By studying its zeros, researchers can pinpoint the critical times when a dynamical phase transition occurs, providing insight into the system's time-dependent critical behavior.

Terminology

Summary

The gist: The competition between Gamma anisotropy and transverse field in an Ising chain leads to vector chiral order and dynamical quantum phase transitions, enriching both equilibrium ordering and dynamical critical behavior

Model Description

The model investigated is a transverse-field Ising chain with dimerized anisotropic Gamma interactions under a transverse magnetic field. The Hamiltonian is given by Hˆ = J X N i=1 σˆ x i σˆ x i+1 + h X N i=1 σˆ z i + X N i=1 J xy i σˆ x i σˆ y i+1 + J yx i σˆ yi σhat xi, where the strength of anisotropic Gamma couplings are taken as J xy i = Γ, J yx i = αΓ for odd i, and J xy i = αΓ, J yx i = Γ for even i. To diagonalize this Hamiltonian, a Jordan-Wigner transformation is introduced to obtain a quadratic fermionic chain with staggered hopping and nearest-neighbor p-wave pairing. The resulting Hamiltonian in the Nambu spinor basis is written in the Bogoliubov-de Gennes (BdG) form Hˆ = 1/2 X k Ψˆ †kHBdG(k)Ψˆk, where HBdG(k) is a specific matrix.

Equilibrium Phase Diagram and Spin Correlations

The study identifies three phases in the equilibrium phase diagram: positive vector chiral phases, negative vector chiral phases, and a paramagnetic phase characterized by the vector spin chirality and the vector chiral order parameter. In the absence of Ising interactions, a gapless critical line is found that exhibits no finite-size drift, where spin correlations and subsystem entanglement entropy display behavior distinct from Ising criticality. Spin-spin correlation functions like Cxxr and the antisymmetric connected spin correlation function Cxyr show spatial dependence on distance r and sublattice parity. For instance, at h = 0.5, both α = 0.5 and α = 1.5 exhibit long-range, period-two oscillations in Cxxr with opposite signs for even and odd separations. The staggered chiral order parameter Oxystag is introduced to characterize the quantum phase by relating it to Cxyr as Oxystag = (-1) i Cxyr=1 (23).

Quantum Criticality and Dynamical Phase Transitions

Dynamical Quantum Phase Transitions (DQPTs) are investigated by analyzing the Loschmidt amplitude G(t), which can be factorized over independent momentum sectors due to lattice momentum conservation. The critical condition for DQPTs is determined by the condition of Loschmidt zeros, where Re Gkc(tc) = 0 and Im Gkc(tc) = 0. The critical times of DQPTs form periodic or aperiodic sequences depending on the quench path. The equal spacing of critical time can arise when the Loschmidt zeros are governed by a single effective two-level sector at a fixed critical momentum in four-band models.

Critical Exponents and Entanglement

The behavior of the vector spin chirality exhibits an algebraic decay at all three critical points, Cxyr ∼ Ar−η, where η is found to be approximately 1/4 for α = 0.5. Subsystem entanglement entropy SL grows logarithmically with the subsystem size L in the bulk interval, following the form SL = c 3 lnL + s0. The extracted central charges are c ≃ 1/2 for both critical points at α = 0.5, consistent with Ising criticality. However, at the critical line α = −1 in the absence of Ising interaction, the excitation spectrum exhibits two gapless nodes with linear dispersion in their vicinity.

Conclusion

The study concludes that dimerized off-diagonal exchange enriches both equilibrium ordering and dynamical critical behavior in a quantum Ising chain. The findings establish dimerized off-diagonal exchange as a mechanism for enriching both the equilibrium phase structure and the dynamical critical behavior of quantum Ising chains.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (Grants No. 12505015, No. 12404493), the Guangdong Basic and Applied Basic Research Foundation (Grants No. 2024A1515110222).

REFERENCES

[8] W.-L. You, Y. Wang, T.-C. Yi, C. Zhang, and A. M. Ole´s, Quantum coherence in a compass chain under an alternating magnetic field, Phys. Rev. B 97, 224420 (2018)

[11] E Solano-Carrillo, R Franco, and J Silva-Valencia, Real-time dynamics of a spin chain with DzyaloshinskiiMoriya interactions: Spiral formation and quantum spin oscillations, Phys. Rev. B:Condens. Matter Mater. Phys. 84, 064426 (2011)

[37] M Heyl, A Polkovnikov, and S Kehrein, Dynamical Quantum Phase Transitions in the Transverse-Field Ising Model, Phys. Rev. Lett. 110, 135704 (2013)

[68] C B Mendl and J C Budich, Stability of dynamical quantum phase transitions in quenched topological insulators: From multiband to disordered systems, Phys. Rev. B 100, 224307 (2019)

[57] S Vajna and B D´ora, Disentangling dynamical phase transitions from equilibrium phase transitions, Phys. Rev. B 89, 161105 (2014), 1401.2865

[39] K Yang, L Zhou, W Ma, X Kong, P Wang, X Qin, X Rong, Y Wang, F Shi, J Gong et al., Floquet dynamical quantum phase transitions, Phys. Rev. B 100 085308 (2019)

[69] K Cao, H Guo, and G Yang, Aperiodic dynamical quantum phase transition in multi-band Bloch Hamiltonian and its origin, J. Phys.:Condens. Matter 36 155401 (2024)

[38] M Heyl, Dynamical quantum phase transitions: a review, Rep. Prog. Phys. 81, 054001 (2018)

[67] P Calabrese and J Cardy, Entanglement entropy and quantum field theory, J Stat. Mech.:Theory Exp. 2004, P06002 (2004)

[59] I M Lifshitz, Anomalies of Electron Characteristics of a Metal in the High Pressure Region, Soviet Physics JETP 11, 1130 (1960)

[64] G C Wick, The Evaluation of the Collision Matrix, Phys. Rev. 80, 268 (1950)

[32] E S Sørensen, J Gordon, J Riddell, T Wang, and H Y Kee, Field-induced chiral soliton phase in the Kitaev spin chain, Phys. Rev. Res. 5 L012027 (2023)

[61] M Rodney, H F Song, S S Lee, K Le Hur, and E S Sørensen, Scaling of entanglement entropy across Lifshitz transitions, Phys. Rev. B 87 115132 (2013)

[44] C Morris, N Desai, J Viirok, D H¨uvonen, U Nagel, T R˜o˜om, J Krizan, R J Cava, T McQueen S Koohpayeh et al., Duality and domain wall dynamics in a twisted Kitaev chain, Nat. Phys.

Improvements for AI systems

  1. textbf Real-time Dynamical Criticality Prediction for Quantum Systems: The improved system can predict critical times of dynamical quantum phase transitions (DQPTs) based on quench paths, as the paper demonstrates that the critical times of dynamical quantum phase transitions form periodic or aperiodic sequences, depending on the quench path.

  2. textbf Enhanced Phase Classification via Vector Chirality: The system can distinguish between different phases by calculating the vector spin chirality and the vector chiral order parameter, allowing it to classify states as positive, negative, or paramagnetic phases.

  3. textbf Novel Correlation Analysis in Critical Regimes: The improved system can analyze correlation functions like spin-spin correlation functions and subsystem entanglement entropy to characterize critical lines, noting that for certain points the excitation spectrum exhibits two gapless nodes at k = ±k0, which corresponds to a massless Dirac low-energy description.

  4. textbf Topological Criticality Identification: The system can identify specific topological features, such as the transition from linear dispersion to quadratic dispersion at the boundary of a Lifshitz critical line, where the low-energy dispersion becomes E+(k) ≃ Γ squared k squared.

Sources

Related papers