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The Zero-Temperature Phase Transition Revealed by a Quantum Computer Challenges Physics Predictions

A multinational group of researchers has successfully simulated spontaneous symmetry breaking (SSB) at zero temperature for the first time, marking an important milestone in condensed matter physics and quantum computing. This groundbreaking work on phase transitions in short-range interactions used a superconducting quantum processor with over 80% fidelity. Researchers from Brazil’s Federal University of São Carlos (UFSCar), Denmark’s Aarhus University, and China’s Southern University of Science and Technology published their findings in Nature Communications.

Spontaneous symmetry breaking, a phenomenon essential to condensed matter physics and the standard model, was the central idea of the experiment. In physical systems, symmetry results in conservation laws, but when it breaks, complex structures can form. For short-range interacting systems at any finite temperature in low dimensions (one or two dimensions), the production of ordered phases such as ferromagnetism (FM) and antiferromagnetism (AFM) is traditionally prohibited by the Mermin-Wagner theorem. For one-dimensional systems, it was widely accepted that Spontaneous Symmetry Breaking was prohibited even at zero temperature.

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What is Spontaneous Symmetry Breaking

The standard model and condensed matter physics both rely on the fundamental mechanism known as spontaneous symmetry breaking (SSB). The nature of physical systems and the emergence of complex structures are closely related to this idea.

Here is a thorough description of Spontaneous Symmetry Breaking derived from the references given:

Core Concept:

• In most physical systems, conservation laws result from symmetry. Noether’s theorem, for instance, captures this connection between conservation and symmetry.
• On the other hand, complex structures can arise when symmetry is broken. The phenomenon known as Spontaneous Symmetry Breaking happens when a system’s ground state or lowest-energy state spontaneously changes to a state that lacks the same symmetry as its governing laws.

Traditional Understanding and Challenges (Mermin-Wagner Theorem):

• Spontaneous Symmetry Breaking in low-dimensional (one and two-dimensional) systems is a topic of great interest for quantum phase transitions at limiting temperatures. It is known that when the physical system contains interactions that are long enough in distance, long-range order, such as ferromagnetism (FM) or antiferromagnetism (AFM), usually arises.
• Specifically, for short-range interacting systems in one or two dimensions, the Mermin-Wagner theorem prohibits the creation of correlated antiferromagnetic (AFM) and ferromagnetic (FM) states at any finite temperature. A broad variety of systems, including as Hubbard and Kondo lattices, spin systems characterised by Heisenberg chains, and interacting electrons in metals, are covered by this theorem.
• It has been thought that Spontaneous Symmetry Breaking is prohibited for one-dimensional systems, even at zero temperature. Compared to its equivalent at finite temperature, this field has received less attention.

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The Experiment’s Breakthrough in Observing SSB:

• The new study represents the first time Spontaneous Symmetry Breaking has been experimentally simulated at zero temperature. utilizing more than 80% fidelity, this was accomplished utilizing a superconducting quantum processor.
• This study’s key focus was on reproducing dynamics at zero temperature, which is physically impossible in the real world (according to the unattainability principle, the third law of thermodynamics). What would occur at absolute zero was simulated using quantum computer resources.
• The experiment showed that even in local particle interactions, i.e., between first neighbours, symmetry breaking can be observed when the temperature is adjusted to zero. For short-range interacting systems at any finite temperature, this contradicts the conventional physics predictions that certain phases are prohibited.

How SSB Manifested in the Experiment:

• The system was powered by a digital quantum annealing algorithm and consisted of seven qubits placed in a superconducting lattice that resembled a three-generation Cayley tree (allowing only nearest-neighbor interactions).
• The initial state was a classical antiferromagnetic (AFM) state, a “flip-flop configuration” in which the spins of the particles alternate between one direction and the other. “Classical Néel state” was the definition given to the initial state.
• After then, the system spontaneously changed and reorganised into a ferromagnetic (FM) quantum state, in which quantum correlations were established and the spins of all the particles lined up in the same direction.
• It explicitly attributes this phase transition from the initial classical AFM state to a quantum FM-like state. The AFM phase emerged when starting from the ground state of the Néel field Hamiltonian, whereas an ordered quantum FM-like state emerged when starting from the excited state. Observations revealed that the system’s energy split was caused by the creation of either FM-like or AFM-like phases, depending on the initial Néel state.

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Role of Symmetry in System Dynamics:

• The initial Hamiltonian for the Néel state has a symmetry in (\hat{M}{z}) (total magnetization), meaning ([\hat{H}{\text{Néel}}, \hat{M}_{z}]=0)21.
• This implies that each adiabatic evolution from the ground or excited Néel states will occur over a different magnetization plane. The ground state has a negative magnetization, while the excited state has a positive magnetization.
• Furthermore, the system also conserved the parity defined by the operator (\hat{\Pi}_z = \prod \hat{\sigma}_z), as ([\hat{\Pi}_z, \hat{H}(s)]=0)22. This conservation law for parity ensured that degenerated states with different parities could not be mixed during the evolution, preventing the destruction of correlated phases22.

Witnessing and Quantifying SSB and Entanglement:

• Two-point correlation functions were used to identify and quantify the phase transition and the creation of ordered patterns (({C}_{x}^{(i,j)})). The system’s dynamical symmetry breakdown was evident from these functions.
• By examining entanglement entropy, more especially the second-order Rényi entropy, the quantum nature of the observed FM-like and AFM-like phases was brought to light.
• In order to measure the degree of entanglement and its distribution across the components of a quantum system, the Hungarian mathematician Alfréd Rényi developed the Rényi entropy. It acts as an observer of the generation of entanglement between subsystems, even in mixed quantum states. Entanglement is shown by an increase in the Rényi entropy of a subsystem (assuming the entire system is pure).

This work essentially demonstrated how complicated quantum phenomena, such as zero-temperature Spontaneous Symmetry Breaking with nearest-neighbor interactions, which are ordinarily unavailable or prohibited by classical physics, can be simulated by quantum computation, resulting in the development of ordered, entangled quantum phases.

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