#qapt

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A powerful theoretical tool for studying phase transitions in open quantum dynamics systems is the Quantum Contact Process.

What is QCP?

Quantum Contact Process combines quantum coherent and classical incoherent processes. The classic non-equilibrium quantum system has an absorbing state. The classical stochastic system Contact Process belongs to the Directed Percolation (DP) universality class and is known for its critical behaviour. QCP focusses on how quantum fluctuations from coherent spin-flips differ from the classical limit in this transition.

Quantum absorbing phase transitions (QAPT) in QCP are caused by coherent quantum fluctuations and incoherent classical fluctuations. The Lindblad formalism, which characterises the system's dissipative nature, allows adjustment of the relative contributions of quantum coherent and classical incoherent effects.

Quantum Absorbing Phase Transition

A QCP phase transition to an absorbing state occurs. This fluctuationless state is permanent once the system absorbs. The classical regime's DP universality class includes this continuous transition. If quantum coherent effects are included, this transition may change.

Directed Percolation may not be the QCP's universality class, according to study. The shift from second-order (continuous) to first-order (discontinuous) can be influenced by quantum fluctuations. The existence and nature of the absorbing state phase transition have been debated. Researchers conducted real-time numerical simulations to estimate critical exponents and show that some regimes feature continuous transitions.

Dependence on Interaction Range and Geometry

One notable QCP observation is that component contact range greatly affects Quantum Absorbing Phase Transition (QAPT).

Short-Range Interactions: Most QCP research has concentrated on Rydberg atoms' s-excited states causing active states. Here, short-range interactions establish quantum coherence. This design usually provides a one-dimensional second-order QAPT (continuous transition).

When atoms' d-excited states induce active states, long-range interactions must be considered. In this long-range contact scenario, a first-order discontinuous transition may occur in one dimension. The mean-field phase diagram resembles the nearest-neighbor QCP in long-range QCP models, when branching and coagulation occur over large distances. Weak quantum regime transitions are continuous, but strong quantum domain transitions are discontinuous.

Researchers have examined how the system's embedded structure affects the QAPT by using the QCP model on scale-free (SF) networks. Logarithmically with system size, scale-free networks' average node distance fluctuates, suggesting great heterogeneity. By studying the QCP on these networks, researchers may determine how interaction range and connection heterogeneity affect the QAPT. They find that the network's degree exponent creates numerous QAPT types.

Crossover Behaviour and Dimensionality

QCP behaviour is also affected by system dimensionality and initial configuration.

One Dimension (1D): The QCP shows complex crossover events. A critical exponent drops from a quantum value to the classical Directed Percolation (DP) value along a critical line that appears when the process starts in a homogeneous state (all active sites are active). This suggests that the quantum coherence effect still affects the boundary condition.

If the one-dimensional QCP starts from a heterogeneous state (just one site active), the essential exponents match the standard DP values. Long-range interactions exhibit this continuously changing exponent characteristic, similar to classical contact.

This elaborate, peculiar crossover activity does not exist in 2D. No matter the setting, traditional DP behaviour is seen throughout the parameter domain. Depending on whether classical or quantum processes dominate a 2D lattice, the system may nonetheless exhibit a unique non-equilibrium phase transition.

Universal Complexity Classes

The QCP's complex universality is visible in transitional regimes where quantum and classical dynamics compete. The semiclassical technique describes the quantum coherence effect as two successive atoms exciting a nearby atom.

This situation may have a tricritical point due to first- and second-order transitions. Tricritical Directed Percolation (TDP) sometimes contains this bicritical point. A novel universality class has been found at the tricritical point of the long-range QCP model, which differs from the traditional DP model with long-range interactions and the nearest-neighbor QCP.

Study Methods and Environment

Since it is simple, the QCP is a good benchmark problem for studying numerical methods for open quantum non-equilibrium systems. Several advanced numerical simulation approaches are used:

The quantum leap Monte Carlo approach. Tensor network methods. Matrix product states. Time-evolving block decimation algorithm.

Neural network, machine learning, finds essential exponents and line.