In open quantum systems, a group of scientists discovered a new kind of phase transition known as quantum strong-to-weak spontaneous symmetry breaking (SWSSB), which is triggered only by adjusting the intrinsic Hamiltonian parameters of a material and takes place independent of the external decoherence strength.
disprove the notion that external noise must be the driving force for such transitions in practical, noisy quantum systems. This finding establishes a new standard for examining robust quantum events in systems that are by nature open.
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Symmetry in Noisy Reality
A fundamental component of contemporary physics, symmetry underlies everything from the Higgs mechanism to crystal formation and is necessary for categorizing quantum phases and comprehending phase transitions. Although isolated (closed) systems benefit much from the conventional notion of symmetry, genuine quantum devices are invariably “open,” undergoing decoherence the loss of quantum coherence brought on by interaction with the environment.
Due to the mixed quantum states created by this interaction, symmetry ideas must be revised. Two fundamental concepts of symmetry are present in open quantum systems: weak symmetry, which only occurs at the ensemble average level, and strong symmetry, which occurs when the state remains invariant under left and right unitary operations (typical of pure states).
Strong-to-weak spontaneous symmetry breaking (SWSSB) is the change from a state that preserves strong symmetry to one that only preserves weak symmetry. Theoretical research on SWSSB usually attributed this thermal phase change to growing decoherence. However, regulating or quantifying decoherence in experimental setups makes it difficult to consistently observe these transitions.
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The Quantum Distinction
A basic question was raised by the researchers Yuxuan Guo, Sheng Yang, and Xue-Jia Yu: Is it possible for SWSSB to take place in a really quantum domain, powered by readily adjustable Hamiltonian parameters, while maintaining the symmetry of the surrounding environment?
Their research reveals a purely quantum SWSSB transition, providing an affirmative response to this query. The open-system analogue of a typical zero-temperature quantum phase transition, this transition is achieved by changing couplings within the Hamiltonian.
The one-dimensional XXZ critical spin chain, a paradigm for frustrated spin systems whose low-energy physics may be explained by Luttinger liquid theory, was the subject of their study. Local quantum channels, specifically two-site XX decoherence, were used to describe the decoherence in order to precisely maintain the global strong symmetry.
Their investigation, which included large-scale numerical simulations using Matrix Product States (MPS) and field theory calculations (using the Choi-Jamiołkowski isomorphism and bosonization techniques), showed two distinct phases separated by a critical line:
- Trivial Luttinger Liquid Phase: The high symmetry of the underlying pure state is resistant against arbitrarily massive symmetry-respecting noise for one area of Hamiltonian parameters, which corresponds to the Luttinger parameter.
- SWSSB Phase: In another region, only weak symmetry is retained when a negligible quantity of noise is enough to break the strong symmetry.
Boundary BKT Criticality
These two regimes are separated by a continuous phase boundary that appears at. This boundary’s membership in the boundary Berezinskii-Kosterlitz-Thouless (BKT) universality class, which is distinguished by an exponentially divergent correlation length, is confirmed by renormalization group (RG) analysis. This critical point is inherent to the open setting since it is specific to the open quantum system and does not exist in the noiseless limit.
The formation of long-range order in the Rényi-2 correlator, a metric useful for differentiating between these mixed-state phases, is a characteristic of the transition. Since symmetry-preserving decoherence in this context does not alter standard correlation functions, the Rényi-2 correlator is preferred.
Additionally, entropic quantities and the notion of local recoverability were used to analyze the stability of the phases from the standpoint of quantum information. The decohered state cannot be locally restored to the initial pure Luttinger liquid phase in the SWSSB phase. The decoherence strength at criticality causes a continuous variation in the effective central charge of the Choi state, which is the doubled Hilbert space representation of the density matrix.
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Broad Applicability and Experimental Promise
The work verified that no SWSSB phase transition is seen within the critical XXZ regime under two-site ZZ decoherence, in contrast to the XX decoherence results. This unfavorable outcome supports the theoretical framework even more.
As long as they are exposed to arbitrary symmetry-preserving decoherence channels, the unified theoretical framework created in this work can be applied to a broad class of one-dimensional quantum systems, such as spin chains and fermionic systems whose low-energy physics is described by Luttinger liquid theory.
It has a good chance of being realized experimentally. In real material or quantum platforms, it is significantly easier to modify Hamiltonian parameters than decoherence channels. Quantum circuits can be used to prepare states efficiently. It is now possible to observe and characterize this purely quantum SWSSB event on near-future quantum devices despite the fact that Rényi-2 correlators cannot be directly measured with detection systems that use randomized measurements.
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