### What is quantum matter?

It may depend on who you ask.

It is interesting that even twenty years ago the phrase "quantum matter" was rarely used.

Now we have

So, what is quantum matter?

It is interesting that even twenty years ago the phrase "quantum matter" was rarely used.

Now we have

*Department of Quantum Matter, Hiroshima University*

*Quantum Matter Institute, University of British Columbia*

*Shoenberg Laboratory for Quantum Matter, University of Cambridge*So, what is quantum matter?

To some it is any material system (solid, liquid, or gas) where the quantum statistics of the constituent particles significantly affect the properties of the system. One could argue on some level this is any state of matter! After all, the Pauli exclusion principle is key to chemistry!

The above departments are largely concerned with studying what used to be called "strongly correlated electron systems". Hence, one also often sees the phrase "correlated quantum matter". I think David Pines and Piers Coleman may be two of the people who have most promoted the phrase. Coleman and Andy Schofield use the phrase "quantum matter" repeatedly in their 2005 Nature review Quantum criticality. Pines has a nice tutorial article Emergent behavior in quantum matter.

Does anyone have a better etymology?

Does anyone have a better etymology?

To me the key idea is that there are states of matter [quantum many-body systems] with

The notion of quantum matter is useful as a unifying concept for describing many of the common themes of interest in two culturally distinct research communities: those studying ultracold atomic gases and correlated electron materials.

There is also a puzzling somewhat philosophical question:

Is quantum matter itself emergent or does quantum matter have emergent properties?

**emergent macroscopic properties that are intrinsically quantum mechanical.**Superconductivity is the classic example, being described by a macroscopic quantum mechanical wave function. Furthermore, there may not be broken symmetries. Instead, the many-body states of quantum matter may require concepts such as topological order, the most common examples being found in fractional quantum Hall effect and topological insulators. In some sense different metallic states: bad metals, "quantum critical metals", and the "strange metal" in the cuprates are all quantum matter.The notion of quantum matter is useful as a unifying concept for describing many of the common themes of interest in two culturally distinct research communities: those studying ultracold atomic gases and correlated electron materials.

There is also a puzzling somewhat philosophical question:

Is quantum matter itself emergent or does quantum matter have emergent properties?

I think there are various levels of quantumness that need to be confronted. As you say, at some level all matter is quantum. But there is a certain sense in which a superconductor is more quantum than a liquid crystal. In the former case there are physical observables that have hbar in it (flux quantum). Yet in both these cases one can describe a phase transition to the ordered state in terms of classical ginzburg landau theory. And there is a certain sense in which one can understand the occurence of the broken u(1) symmetry as that the superconductor's phase becomes a classical variable in the same sense that the magnetization of a ferromagnet is a classical variable. At the next level of quantum are systems like metals that can only be written as product states in certain bases (states like superconductors share somewhat these properties, but in a different fashion). And the final and most quantum of states of matter are those states that don't admit a product state description and are highly entangled. Examples of the latter are spin-liquid states.

ReplyDeleteFiner gradation of quantum-ness are probably possible.

There is actually a finer graduation of quantum-ness (along the lines discussed by Peter Armitage above) in the case of gapped states. Actually according to this, topological insulators are not examples of topological order.

ReplyDeleteOne can define the notions of long-range entangled (LRE) states and short-range entangled (SRE) states for gapped systems. A SRE state is a state in which the ground state can be deformed into a product-state (no entanglement) by step by step removing the entanglement locally (for example between nearby sites in a spin system). If a state cannot be turned into a product-state in this way, it is said to be LRE.

There can exit many distinct LRE states which cannot be turned into each-other by changing the local entanglement structure. These distinct classes of states are known as topological order, fractional quantum Hall effect is one example here, another is gapped spin-liquids. Thus different classes of topological order is related to different patterns of (long range) entanglement, or different ways of being quantum.

If one however considers states with symmetries, and only allow for removal of local entanglement that respects the symmetry, then SRE states can also be split into distinct classes. These are known as symmetry protected topological (SPT) states. SPT states generically have interesting edge states which are protected as long as the given symmetry is unbroken. Thus these states are also quantum, but less than LRE states.

For example, the free-fermion topological insulators are SPT states. Meaning that they do not have LRE and topological order (no anyons/topological entanglement entropy, ground state degeneracy on torus etc.). They are only protected from becoming a product state by a symmetry (such as time-reversal symmetry). The same for their edge states.

Another famous example of a SPT state, is the Haldane spin-1 chain. At the edge, it has spin-1/2 excitations which are protected by symmetry.

Similar classification of quantum-ness of gapless states, using patterns of entanglement, seems much more tricky.

Thanks to Peter for raising the important question about levels of "quantum-ness".

DeleteThanks to HM for clarifying this, particularly for the specific case of gapped systems.

HM, what do you think is the clearest article which discusses the distinction between SRE and LRE [i.e. short-range vs. long-range entanglement]?

Great post. I think the sound of a term is important, and the term "Quantum Matter" provides us with a useful counterpoint to "Soft Matter" and "Biological Matter", the three making up the trio of emergent matter types. Of course, the division between the two is extremely fuzzy and no doubt, discoveries in the future will serve to blur the lines further, perhaps requiring new definitions.

ReplyDeleteOf course, everything is quantum, and to my mind, it is quantum mechanics that provides a big part of the canvas on which emergence develops. Classical physics for exampls, is an emergent consequence of quantum mechanics that we take for granted, because this is the world we live in. Superconductivity is a beautiful example of how new kinds of macroscopic behavior (which require h finite), but which are nevertheless described by emergent classical physics, derive from quantum physics.

liquid water may be quantum matter, its structure should be predicted with quantum effects.

ReplyDelete