Researchers reveal Ising model criticality survives decoherence with, and properties

The behaviour of quantum systems as they lose coherence, a process known as decoherence, remains a fundamental question in physics, and recent research sheds new light on this phenomenon within the well-studied Ising model. Yoshihito Kuno from Akita University, Takahiro Orito from Nihon University, and Ikuo Ichinose from Nagoya Institute of Technology, alongside their colleagues, investigate how decoherence impacts the critical properties of this model, revealing a surprising preservation of Ising characteristics even as the system degrades. Their work demonstrates that, up to a certain point, the decohered system retains the hallmarks of a critical phase transition similar to the pure, undisturbed model, exhibiting specific values for key parameters that distinguish it from other known critical states. This discovery is significant because it challenges the expectation that decoherence always destroys quantum criticality, and it identifies a threshold beyond which the system undergoes a fundamental shift in its behaviour, transitioning from a subtle preservation of quantum order to a more conventional form of symmetry breaking.

Mixed States, Quantum Criticality and Topology

This research explores the complex behaviour of quantum systems existing as mixed states, subject to environmental noise and decoherence. It investigates quantum criticality, topological phases, and symmetry breaking, moving beyond traditional condensed matter physics which often focuses on idealised, pure ground states. The work examines how these phenomena manifest under realistic conditions and how to characterise these complex states. Researchers are exploring the possibility of entirely new phases of matter that exist only in mixed states, requiring novel characterisation tools. Investigations include how symmetries are broken and whether this leads to new types of order, as well as the possibility of topological phases remaining stable even with decoherence.

Key tools employed include Rényi entropy and mutual information to quantify entanglement and correlation, alongside numerical techniques like Scan Density Matrix Renormalization Group and Tensor Networks. The research delves into core concepts like Tensor Networks, providing graphical representations of quantum states for efficient simulations, and Density Matrix Renormalization Group, a powerful method for finding the ground state of one-dimensional quantum systems. Rényi Entropy and Mutual Information characterise entanglement in mixed states, while the Rényi Markov Length quantifies the range of correlations. The Doubled Space Formalism maps mixed states to pure states in a higher-dimensional space, simplifying analysis.

Conformal Field Theory provides a framework for understanding critical phenomena, and Symmetry Protected Topological phases offer robust, exotic properties. Specific research directions include assessing the robustness of topological phases, investigating spontaneous symmetry breaking in mixed states, and identifying new phase transitions that occur only in mixed states. The work develops new tools to characterise these phases, including Rényi entropy, mutual information, and tensor networks, and explores the connection between mixed state phases and conformal field theory. The importance of symmetry in protecting topological phases and stabilising mixed state phases is also emphasised, alongside the use of purification techniques to understand the properties of mixed states.

Decoherence and Criticality in the Ising Model

Researchers investigated criticality in the Ising model when subjected to decoherence, a process introducing mixed states. They employed the Doubled Hilbert Space Formalism, a method for representing mixed states, alongside Matrix Product States to perform extensive computational studies. This approach allowed them to explore how decoherence affects the critical properties of the system, specifically whether characteristics of the pure Ising model are preserved. The methodology involves simulating the effects of decoherence, the loss of quantum information, using an X + ZZ decoherence channel, mimicking environmental interactions.

Researchers then calculated the Rényi-2 subsystem entanglement entropy, a measure of quantum entanglement within a portion of the system, and examined its scaling behaviour. This involved a numerical filtering operation applied to the Matrix Product States, enabling precise calculations even with decoherence. A key innovation lies in applying the Doubled Hilbert Space Formalism to the Matrix Product States calculations, effectively expanding the computational space for accurate representation of mixed states. Scientists focused on the subleading term in the scaling of the Rényi-2 mutual information to determine the central charge, a crucial parameter characterising the critical behaviour. They discovered that, up to a moderate level of decoherence, the mixed states retained the properties of the Ising Conformal Field Theory, exhibiting a central charge consistent with the pure Ising model. However, beyond a certain threshold, the decoherence washed out the Ising criticality, leading to a transition to a state with strong-to-weak spontaneous symmetry breaking.

Decoherence Drives Ising Model to Ashkin-Teller

Researchers investigated criticality in the Ising model when subjected to decoherence, a process where quantum information is lost due to environmental interactions. They employed the Doubled Hilbert Space Formalism, a mathematical technique creating a mirrored version of the quantum system’s state, to analyse how decoherence affects the system’s critical behaviour. This revealed that, under specific decoherence conditions, the resulting state aligns with the critical line of the Ashkin-Teller model, a related system in physics. The team discovered that even with weak decoherence, the Ising model retains partial characteristics of its original critical state, demonstrating a surprising resilience to environmental noise.

Extensive numerical studies, utilising both the Doubled Hilbert Space Formalism and Matrix Product States, confirmed that the system exhibits properties consistent with the Ising Conformal Field Theory up to moderate levels of decoherence. Specifically, they measured a central charge and critical exponents, values that distinctly differ from those predicted by the orbifold boson conformal field theory. Further analysis identified a threshold beyond which decoherence overwhelms the remnant Ising criticality, inducing a transition to a strong-to-weak spontaneous symmetry breaking phase. This signifies a fundamental change in the system’s behaviour, where the original order parameter weakens and a new, less pronounced order emerges. The research demonstrates that the Doubled Hilbert Space Formalism provides a valuable tool for understanding the behaviour of mixed quantum states under decoherence, offering insights into the preservation and eventual loss of critical behaviour in complex systems.

Decoherence Preserves Ising Model Criticality

This research investigates criticality in the Ising model when subjected to decoherence, a process introducing mixed states into a quantum system. The team demonstrates that under specific decoherence conditions, the resulting mixed state resides on a critical line closely related to the Ashkin-Teller model, while still retaining aspects of the original Ising model’s criticality. This preservation of criticality occurs because the mixed state satisfies a particular self-duality condition.